Deck 2: Matrices

ملء الشاشة (f)
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سؤال
If possible, find <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible <div style=padding-top: 35px> . <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible <div style=padding-top: 35px> , <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible <div style=padding-top: 35px>

A) <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible <div style=padding-top: 35px>
B) <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible <div style=padding-top: 35px>
C) <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible <div style=padding-top: 35px>
D) <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible <div style=padding-top: 35px>
E) not possible
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سؤال
Use the following matrices to perform the indicated matrix operations, if possible. <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Find <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> . <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
If possible, find <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible <div style=padding-top: 35px> . <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible <div style=padding-top: 35px> , <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible <div style=padding-top: 35px>

A) <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible <div style=padding-top: 35px>
B) <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible <div style=padding-top: 35px>
C) <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible <div style=padding-top: 35px>
D) <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible <div style=padding-top: 35px>
E) not possible
سؤال
Use the following matrices to perform the indicated matrix operations, if possible. <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Use the following matrices to perform the indicated matrix operations, if possible. <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Use the matrices to find CD, if possible. <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Use the matrices below. Perform the indicated operation.
AB <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px> , <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px>
سؤال
Use the matrices below. Perform the indicated operations.
BA <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Multiply the matrices. <strong>Multiply the matrices.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Multiply the matrices.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Multiply the matrices.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Multiply the matrices.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Multiply the matrices.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Multiply the matrices.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Indicate whether the statement "If A is a Indicate whether the statement If A is a   matrix and B is a   matrix, then the product   is a   matrix.is <div style=padding-top: 35px> matrix and B is a Indicate whether the statement If A is a   matrix and B is a   matrix, then the product   is a   matrix.is <div style=padding-top: 35px> matrix, then the product Indicate whether the statement If A is a   matrix and B is a   matrix, then the product   is a   matrix.is <div style=padding-top: 35px> is a Indicate whether the statement If A is a   matrix and B is a   matrix, then the product   is a   matrix.is <div style=padding-top: 35px> matrix."is
سؤال
Solve <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> for X when <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> and <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Find B(CA), provided that <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Find (B+C)A, provided that <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Find <strong>Find   . (Note: A<sup>2</sup> = AA.)   </strong> A)    B)    C)    D)    E) not possible <div style=padding-top: 35px> . (Note: A2 = AA.) <strong>Find   . (Note: A<sup>2</sup> = AA.)   </strong> A)    B)    C)    D)    E) not possible <div style=padding-top: 35px>

A) <strong>Find   . (Note: A<sup>2</sup> = AA.)   </strong> A)    B)    C)    D)    E) not possible <div style=padding-top: 35px>
B) <strong>Find   . (Note: A<sup>2</sup> = AA.)   </strong> A)    B)    C)    D)    E) not possible <div style=padding-top: 35px>
C) <strong>Find   . (Note: A<sup>2</sup> = AA.)   </strong> A)    B)    C)    D)    E) not possible <div style=padding-top: 35px>
D) <strong>Find   . (Note: A<sup>2</sup> = AA.)   </strong> A)    B)    C)    D)    E) not possible <div style=padding-top: 35px>
E) not possible
سؤال
Find <strong>Find   if   </strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px> if <strong>Find   if   </strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Find   if   </strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Find   if   </strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Find   if   </strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Find   if   </strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Find   if   </strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Write the transpose of matrix A. <strong>Write the transpose of matrix A.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Write the transpose of matrix A.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Write the transpose of matrix A.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Write the transpose of matrix A.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Write the transpose of matrix A.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Write the transpose of matrix A.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Find (AB) if <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> and <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Consider the matrices <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> . Find scalars a and b such that <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> .

A) <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Use the provided definition to find f(A): If f is the polynomial function, <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , then for an <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> matrix A, f ( A ) is defined to be <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> . Given that <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> .

A) <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
If If   and   , are C and D inverse matrices<div style=padding-top: 35px> and If   and   , are C and D inverse matrices<div style=padding-top: 35px> , are C and D inverse matrices
سؤال
Find the inverse matrix, if one exists. <strong>Find the inverse matrix, if one exists.   </strong> A)   B)    C)   D)    E) no inverse exists <div style=padding-top: 35px>

A) <strong>Find the inverse matrix, if one exists.   </strong> A)   B)    C)   D)    E) no inverse exists <div style=padding-top: 35px>
B) <strong>Find the inverse matrix, if one exists.   </strong> A)   B)    C)   D)    E) no inverse exists <div style=padding-top: 35px>
C) <strong>Find the inverse matrix, if one exists.   </strong> A)   B)    C)   D)    E) no inverse exists <div style=padding-top: 35px>
D) <strong>Find the inverse matrix, if one exists.   </strong> A)   B)    C)   D)    E) no inverse exists <div style=padding-top: 35px>
E) no inverse exists
سؤال
Find the inverse of the matrix <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Given matrix <strong>Given matrix   . Find A<sup>-1</sup> the inverse matrix.</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> . Find A-1 the inverse matrix.

A) <strong>Given matrix   . Find A<sup>-1</sup> the inverse matrix.</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Given matrix   . Find A<sup>-1</sup> the inverse matrix.</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Given matrix   . Find A<sup>-1</sup> the inverse matrix.</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Given matrix   . Find A<sup>-1</sup> the inverse matrix.</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Given matrix   . Find A<sup>-1</sup> the inverse matrix.</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
<strong>  </strong> A) -1 B) 0 C)    D)    <div style=padding-top: 35px>

A) -1
B) 0
C) <strong>  </strong> A) -1 B) 0 C)    D)    <div style=padding-top: 35px>
D) <strong>  </strong> A) -1 B) 0 C)    D)    <div style=padding-top: 35px>
سؤال
Find the inverse of the matrix <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)   E)    <div style=padding-top: 35px>

A) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)   E)    <div style=padding-top: 35px>
B) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)   E)    <div style=padding-top: 35px>
C) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)   E)    <div style=padding-top: 35px>
D) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)   E)    <div style=padding-top: 35px>
E) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)   E)    <div style=padding-top: 35px>
سؤال
Given that matrix <strong>Given that matrix   . Find the inverse matrix.</strong> A)    B)    C)    D)    E)   <div style=padding-top: 35px> . Find the inverse matrix.

A) <strong>Given that matrix   . Find the inverse matrix.</strong> A)    B)    C)    D)    E)   <div style=padding-top: 35px>
B) <strong>Given that matrix   . Find the inverse matrix.</strong> A)    B)    C)    D)    E)   <div style=padding-top: 35px>
C) <strong>Given that matrix   . Find the inverse matrix.</strong> A)    B)    C)    D)    E)   <div style=padding-top: 35px>
D) <strong>Given that matrix   . Find the inverse matrix.</strong> A)    B)    C)    D)    E)   <div style=padding-top: 35px>
E) <strong>Given that matrix   . Find the inverse matrix.</strong> A)    B)    C)    D)    E)   <div style=padding-top: 35px>
سؤال
Use inverse matrices to solve the system of linear equations. <strong>Use inverse matrices to solve the system of linear equations.   </strong> A)    B)    C)    D)   E)    <div style=padding-top: 35px>

A) <strong>Use inverse matrices to solve the system of linear equations.   </strong> A)    B)    C)    D)   E)    <div style=padding-top: 35px>
B) <strong>Use inverse matrices to solve the system of linear equations.   </strong> A)    B)    C)    D)   E)    <div style=padding-top: 35px>
C) <strong>Use inverse matrices to solve the system of linear equations.   </strong> A)    B)    C)    D)   E)    <div style=padding-top: 35px>
D) <strong>Use inverse matrices to solve the system of linear equations.   </strong> A)    B)    C)    D)   E)    <div style=padding-top: 35px>
E) <strong>Use inverse matrices to solve the system of linear equations.   </strong> A)    B)    C)    D)   E)    <div style=padding-top: 35px>
سؤال
Use inverse matrices to solve the system of linear equations.<strong>Use inverse matrices to solve the system of linear equations.  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Use inverse matrices to solve the system of linear equations.  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Use inverse matrices to solve the system of linear equations.  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Use inverse matrices to solve the system of linear equations.  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Use inverse matrices to solve the system of linear equations.  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Use inverse matrices to solve the system of linear equations.  </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Use inverse matrices and the graphing calculator to find the solution of the system of equations. <strong>Use inverse matrices and the graphing calculator to find the solution of the system of equations.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Use inverse matrices and the graphing calculator to find the solution of the system of equations.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Use inverse matrices and the graphing calculator to find the solution of the system of equations.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Use inverse matrices and the graphing calculator to find the solution of the system of equations.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Use inverse matrices and the graphing calculator to find the solution of the system of equations.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Use inverse matrices and the graphing calculator to find the solution of the system of equations.   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Let <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> , <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> . Find an elementary matrix E such that <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px> .

A) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Let <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px> , <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px> . Find an elementary matrix E such that <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px> .

A) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px>
B) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px>
C) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px>
D) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px>
E) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px>
سؤال
Find the inverse of the elementary matrix <strong>Find the inverse of the elementary matrix   </strong> A)    B)    C)   D)    E)    <div style=padding-top: 35px>

A) <strong>Find the inverse of the elementary matrix   </strong> A)    B)    C)   D)    E)    <div style=padding-top: 35px>
B) <strong>Find the inverse of the elementary matrix   </strong> A)    B)    C)   D)    E)    <div style=padding-top: 35px>
C) <strong>Find the inverse of the elementary matrix   </strong> A)    B)    C)   D)    E)    <div style=padding-top: 35px>
D) <strong>Find the inverse of the elementary matrix   </strong> A)    B)    C)   D)    E)    <div style=padding-top: 35px>
E) <strong>Find the inverse of the elementary matrix   </strong> A)    B)    C)   D)    E)    <div style=padding-top: 35px>
سؤال
Find the inverse of the matrix <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Find the inverse of the matrix <strong>Find the inverse of the matrix   using elementary matrices.</strong> A)    B)   C)   D)   E)   <div style=padding-top: 35px> using elementary matrices.

A)
<strong>Find the inverse of the matrix   using elementary matrices.</strong> A)    B)   C)   D)   E)   <div style=padding-top: 35px>

B)
<strong>Find the inverse of the matrix   using elementary matrices.</strong> A)    B)   C)   D)   E)   <div style=padding-top: 35px>
C)
<strong>Find the inverse of the matrix   using elementary matrices.</strong> A)    B)   C)   D)   E)   <div style=padding-top: 35px>
D)
<strong>Find the inverse of the matrix   using elementary matrices.</strong> A)    B)   C)   D)   E)   <div style=padding-top: 35px>
E)
<strong>Find the inverse of the matrix   using elementary matrices.</strong> A)    B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Which of the following is a product of elementary matrices for the matrix <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)    D)   E)    <div style=padding-top: 35px>

A) <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)    D)   E)    <div style=padding-top: 35px>
B) <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)    D)   E)    <div style=padding-top: 35px>
C) <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)    D)   E)    <div style=padding-top: 35px>
D) <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)    D)   E)    <div style=padding-top: 35px>
E) <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)    D)   E)    <div style=padding-top: 35px>
سؤال
Which of the following is a product of elementary matrices for the matrix <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A)
<strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B)
<strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C)
<strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D)
<strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E)
<strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Which of the following is the LU-factorization of the matrix <strong>Which of the following is the LU-factorization of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>

A) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)    B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
Which of the following is the LU-factorization of the matrix <strong>Which of the following is the LU-factorization of the matrix   </strong> A)   B)    C)   D)    E)    <div style=padding-top: 35px>

A) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)   B)    C)   D)    E)    <div style=padding-top: 35px>
B) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)   B)    C)   D)    E)    <div style=padding-top: 35px>
C) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)   B)    C)   D)    E)    <div style=padding-top: 35px>
D) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)   B)    C)   D)    E)    <div style=padding-top: 35px>
E) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)   B)    C)   D)    E)    <div style=padding-top: 35px>
سؤال
The market research department at a manufacturing plant determines that 30% of the people who purchase the plant's product during any month will not purchase it the next month. On the other hand, 40% of the people who do not purchase the product during any month will purchase it the next month. In a population of 1000 people, 100 people purchased the product this month. How many will purchase the product next month?

A) 510 people
B) 570 people
C) 430 people
D) 400 people
E) 370 people
سؤال
The market research department at a manufacturing plant determines that 30% of the people who purchase the plant's product during any month will not purchase it the next month. On the other hand, 60% of the people who do not purchase the product during any month will purchase it the next month. In a population of 1000 people, 200 people purchased the product this month. How many will purchase the product in 2 months?

A) 638 people
B) 830 people
C) 744 people
D) 812 people
E) 662 people
سؤال
A population of 10,000 is grouped as follows: 5,000 nonsmokers, 3,500 smokers of one pack or less per day, and 1,500 smokers of more than one pack per day. During any month there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 5% probability of quitting and a 20% probability of dropping to a pack or less per day. How many people will be in each of the three groups in 1 month?

A) The number of people in each group is as follows: 5,475 nonsmokers, 3,150 smokers of one pack or less per day, and 1,375 smokers of more than one pack per day.
B) The number of people in each group is as follows: 4,975 nonsmokers, 3,350 smokers of one pack or less per day, and 1,675 smokers of more than one pack per day.
C) The number of people in each group is as follows: 5,475 nonsmokers, 3,350 smokers of one pack or less per day, and 1,175 mokers of more than one pack per day.
D) The number of people in each group is as follows: 4,975 nonsmokers, 3,150 smokers of one pack or less per day, and 1,875 mokers of more than one pack per day.
E) The number of people in each group is as follows: 4,775 nonsmokers, 1,875 smokers of one pack or less per day, and 3,350 smokers of more than one pack per day.
سؤال
A population of 100,000 consumers is grouped as follows: 20,000 users of Brand A, 30,000 users of Brand B, and 50,000 who use neither brand. During any month a Brand A user has a 20% probability of switching to Brand B and a 10% probability of not using either brand. A Brand B user has a 15% probability of switching to Brand A and a 20% probability of not using either brand. A nonuser has a 20% probability of purchasing Brand A and a 25% probability of purchasing Brand B. How many people will be in each group in 1 month?

A) The number of people in each group is as follows: 30,300 users of Brand A, 36,000 users of Brand B, and 33,700 who use neither brand.
B) The number of people in each group is as follows: 41,700 users of Brand A, 28,500 users of Brand B, and 29,800 who use neither brand.
C) The number of people in each group is as follows: 35,500 users of Brand A, 30,300 users of Brand B, and 34,200 who use neither brand.?
D) The number of people in each group is as follows: 28,500 users of Brand A, 36,000 users of Brand B, and 35,500 who use neither brand.
E) The number of people in each group is as follows: 30,300 users of Brand A, 41,700 users of Brand B, and 28,000 who use neither brand.
سؤال
Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix <strong>Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix   </strong> A)   B)   C)   D)    E)    <div style=padding-top: 35px>

A) <strong>Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix   </strong> A)   B)   C)   D)    E)    <div style=padding-top: 35px>
B) <strong>Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix   </strong> A)   B)   C)   D)    E)    <div style=padding-top: 35px>
C) <strong>Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix   </strong> A)   B)   C)   D)    E)    <div style=padding-top: 35px>
D) <strong>Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix   </strong> A)   B)   C)   D)    E)    <div style=padding-top: 35px>
E) <strong>Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix   </strong> A)   B)   C)   D)    E)    <div style=padding-top: 35px>
سؤال
Find <strong>Find   of the matrix   to decode the cryptogram. 11 , 21 , 64 , 112 , 25 , 50 , 29 , 49 , 78 , 136 , 20 , 36 , 76 , 127</strong> A) HAPPY_NEW_YEAR B) MEET_ME_FRIDAY C) MEET_ME_SUNDAY D) MEET_ME_MONDAY E) HAPPY_BIRTHDAY <div style=padding-top: 35px> of the matrix <strong>Find   of the matrix   to decode the cryptogram. 11 , 21 , 64 , 112 , 25 , 50 , 29 , 49 , 78 , 136 , 20 , 36 , 76 , 127</strong> A) HAPPY_NEW_YEAR B) MEET_ME_FRIDAY C) MEET_ME_SUNDAY D) MEET_ME_MONDAY E) HAPPY_BIRTHDAY <div style=padding-top: 35px> to decode the cryptogram. 11 , 21 , 64 , 112 , 25 , 50 , 29 , 49 , 78 , 136 , 20 , 36 , 76 , 127

A) HAPPY_NEW_YEAR
B) MEET_ME_FRIDAY
C) MEET_ME_SUNDAY
D) MEET_ME_MONDAY
E) HAPPY_BIRTHDAY
سؤال
A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px> where the external demand is <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px> . Round all the entries of the matrix to two decimal places, where applicable.

A) <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px>
B) <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px>
C) <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px>
D) <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px>
E) <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)    <div style=padding-top: 35px>
سؤال
A small community includes a farmer, a baker, and a grocer and has the input-output matrix <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px>
and external demand matrix <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px> . Solve for the output matrix X in the equation <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px> .

A) <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px>
B) <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px>
C) <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px>
D) <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px>
E) <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)    <div style=padding-top: 35px>
سؤال
Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places <strong>Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places  </strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px>

A) <strong>Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places  </strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px>
B) <strong>Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places  </strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px>
C) <strong>Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places  </strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px>
D) <strong>Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places  </strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px>
E) <strong>Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places  </strong> A)    B)   C)    D)   E)    <div style=padding-top: 35px>
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Deck 2: Matrices
1
If possible, find <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible . <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible , <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible

A) <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible
B) <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible
C) <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible
D) <strong>If possible, find   .   ,   </strong> A)    B)   C)    D)    E) not possible
E) not possible

2
Use the following matrices to perform the indicated matrix operations, if possible. <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    , <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)

A) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)
B) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)
C) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)
D) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)
E) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)

3
Find <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)    . <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)    , <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)

A) <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)
B) <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)
C) <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)
D) <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)
E) <strong>Find   .   ,   </strong> A)    B)    C)    D)    E)

4
If possible, find <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible . <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible , <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible

A) <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible
B) <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible
C) <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible
D) <strong>If possible, find   .   ,   </strong> A)    B)    C)   D)    E) not possible
E) not possible
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5
Use the following matrices to perform the indicated matrix operations, if possible. <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)    <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)    , <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)

A) <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)
B) <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)
C) <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)
D) <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)
E) <strong>Use the following matrices to perform the indicated matrix operations, if possible.     ,  </strong> A)    B)    C)    D)    E)
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6
Use the following matrices to perform the indicated matrix operations, if possible. <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)    , <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)

A) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)
B) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)
C) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)
D) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)
E) <strong>Use the following matrices to perform the indicated matrix operations, if possible.      ,   </strong> A)    B)    C)    D)    E)
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7
Use the matrices to find CD, if possible. <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)    , <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)

A) <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)
B) <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)
C) <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)
D) <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)
E) <strong>Use the matrices to find CD, if possible.   ,   </strong> A)    B)    C)    D)    E)
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8
Use the matrices below. Perform the indicated operation.
AB <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)    , <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)

A) <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)
B) <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)
C) <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)
D) <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)
E) <strong>Use the matrices below. Perform the indicated operation. AB   ,   </strong> A)    B)   C)    D)    E)
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9
Use the matrices below. Perform the indicated operations.
BA <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)    , <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)

A) <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)
B) <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)
C) <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)
D) <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)
E) <strong>Use the matrices below. Perform the indicated operations. BA   ,  </strong> A)    B)    C)    D)    E)
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10
Multiply the matrices. <strong>Multiply the matrices.   </strong> A)    B)    C)    D)    E)

A) <strong>Multiply the matrices.   </strong> A)    B)    C)    D)    E)
B) <strong>Multiply the matrices.   </strong> A)    B)    C)    D)    E)
C) <strong>Multiply the matrices.   </strong> A)    B)    C)    D)    E)
D) <strong>Multiply the matrices.   </strong> A)    B)    C)    D)    E)
E) <strong>Multiply the matrices.   </strong> A)    B)    C)    D)    E)
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11
Indicate whether the statement "If A is a Indicate whether the statement If A is a   matrix and B is a   matrix, then the product   is a   matrix.is matrix and B is a Indicate whether the statement If A is a   matrix and B is a   matrix, then the product   is a   matrix.is matrix, then the product Indicate whether the statement If A is a   matrix and B is a   matrix, then the product   is a   matrix.is is a Indicate whether the statement If A is a   matrix and B is a   matrix, then the product   is a   matrix.is matrix."is
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12
Solve <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)    for X when <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)    and <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)

A) <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)
B) <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)
C) <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)
D) <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)
E) <strong>Solve   for X when   and   </strong> A)    B)    C)    D)    E)
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13
Find B(CA), provided that <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)    , <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)    , <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)

A) <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)
B) <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)
C) <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)
D) <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)
E) <strong>Find B(CA), provided that   ,   ,  </strong> A)    B)    C)    D)    E)
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14
Find (B+C)A, provided that <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)    , <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)    , <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)

A) <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)
B) <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)
C) <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)
D) <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)
E) <strong>Find (B+C)A, provided that   ,   ,   </strong> A)    B)    C)    D)    E)
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15
Find <strong>Find   . (Note: A<sup>2</sup> = AA.)   </strong> A)    B)    C)    D)    E) not possible . (Note: A2 = AA.) <strong>Find   . (Note: A<sup>2</sup> = AA.)   </strong> A)    B)    C)    D)    E) not possible

A) <strong>Find   . (Note: A<sup>2</sup> = AA.)   </strong> A)    B)    C)    D)    E) not possible
B) <strong>Find   . (Note: A<sup>2</sup> = AA.)   </strong> A)    B)    C)    D)    E) not possible
C) <strong>Find   . (Note: A<sup>2</sup> = AA.)   </strong> A)    B)    C)    D)    E) not possible
D) <strong>Find   . (Note: A<sup>2</sup> = AA.)   </strong> A)    B)    C)    D)    E) not possible
E) not possible
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16
Find <strong>Find   if   </strong> A)   B)    C)    D)    E)    if <strong>Find   if   </strong> A)   B)    C)    D)    E)

A) <strong>Find   if   </strong> A)   B)    C)    D)    E)
B) <strong>Find   if   </strong> A)   B)    C)    D)    E)
C) <strong>Find   if   </strong> A)   B)    C)    D)    E)
D) <strong>Find   if   </strong> A)   B)    C)    D)    E)
E) <strong>Find   if   </strong> A)   B)    C)    D)    E)
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17
Write the transpose of matrix A. <strong>Write the transpose of matrix A.   </strong> A)    B)    C)    D)    E)

A) <strong>Write the transpose of matrix A.   </strong> A)    B)    C)    D)    E)
B) <strong>Write the transpose of matrix A.   </strong> A)    B)    C)    D)    E)
C) <strong>Write the transpose of matrix A.   </strong> A)    B)    C)    D)    E)
D) <strong>Write the transpose of matrix A.   </strong> A)    B)    C)    D)    E)
E) <strong>Write the transpose of matrix A.   </strong> A)    B)    C)    D)    E)
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18
Find (AB) if <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)    and <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)

A) <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)
B) <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)
C) <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)
D) <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)
E) <strong>Find (AB) if   and   </strong> A)    B)    C)    D)    E)
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19
Consider the matrices <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)    , <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)    , <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)    . Find scalars a and b such that <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)    .

A) <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)
B) <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)
C) <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)
D) <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)
E) <strong>Consider the matrices   ,   ,   . Find scalars a and b such that   .</strong> A)    B)    C)    D)    E)
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Use the provided definition to find f(A): If f is the polynomial function, <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    , then for an <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    matrix A, f ( A ) is defined to be <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    . Given that <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    , <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)    .

A) <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)
B) <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)
C) <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)
D) <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)
E) <strong>Use the provided definition to find f(A): If f is the polynomial function,   , then for an   matrix A, f ( A ) is defined to be   . Given that   ,   .</strong> A)    B)    C)    D)    E)
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21
If If   and   , are C and D inverse matrices and If   and   , are C and D inverse matrices , are C and D inverse matrices
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22
Find the inverse matrix, if one exists. <strong>Find the inverse matrix, if one exists.   </strong> A)   B)    C)   D)    E) no inverse exists

A) <strong>Find the inverse matrix, if one exists.   </strong> A)   B)    C)   D)    E) no inverse exists
B) <strong>Find the inverse matrix, if one exists.   </strong> A)   B)    C)   D)    E) no inverse exists
C) <strong>Find the inverse matrix, if one exists.   </strong> A)   B)    C)   D)    E) no inverse exists
D) <strong>Find the inverse matrix, if one exists.   </strong> A)   B)    C)   D)    E) no inverse exists
E) no inverse exists
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23
Find the inverse of the matrix <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)

A) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)
B) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)
C) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)
D) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)
E) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)
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24
Given matrix <strong>Given matrix   . Find A<sup>-1</sup> the inverse matrix.</strong> A)    B)    C)    D)    E)    . Find A-1 the inverse matrix.

A) <strong>Given matrix   . Find A<sup>-1</sup> the inverse matrix.</strong> A)    B)    C)    D)    E)
B) <strong>Given matrix   . Find A<sup>-1</sup> the inverse matrix.</strong> A)    B)    C)    D)    E)
C) <strong>Given matrix   . Find A<sup>-1</sup> the inverse matrix.</strong> A)    B)    C)    D)    E)
D) <strong>Given matrix   . Find A<sup>-1</sup> the inverse matrix.</strong> A)    B)    C)    D)    E)
E) <strong>Given matrix   . Find A<sup>-1</sup> the inverse matrix.</strong> A)    B)    C)    D)    E)
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25
<strong>  </strong> A) -1 B) 0 C)    D)

A) -1
B) 0
C) <strong>  </strong> A) -1 B) 0 C)    D)
D) <strong>  </strong> A) -1 B) 0 C)    D)
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26
Find the inverse of the matrix <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)   E)

A) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)   E)
B) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)   E)
C) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)   E)
D) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)   E)
E) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)   E)
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27
Given that matrix <strong>Given that matrix   . Find the inverse matrix.</strong> A)    B)    C)    D)    E)   . Find the inverse matrix.

A) <strong>Given that matrix   . Find the inverse matrix.</strong> A)    B)    C)    D)    E)
B) <strong>Given that matrix   . Find the inverse matrix.</strong> A)    B)    C)    D)    E)
C) <strong>Given that matrix   . Find the inverse matrix.</strong> A)    B)    C)    D)    E)
D) <strong>Given that matrix   . Find the inverse matrix.</strong> A)    B)    C)    D)    E)
E) <strong>Given that matrix   . Find the inverse matrix.</strong> A)    B)    C)    D)    E)
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28
Use inverse matrices to solve the system of linear equations. <strong>Use inverse matrices to solve the system of linear equations.   </strong> A)    B)    C)    D)   E)

A) <strong>Use inverse matrices to solve the system of linear equations.   </strong> A)    B)    C)    D)   E)
B) <strong>Use inverse matrices to solve the system of linear equations.   </strong> A)    B)    C)    D)   E)
C) <strong>Use inverse matrices to solve the system of linear equations.   </strong> A)    B)    C)    D)   E)
D) <strong>Use inverse matrices to solve the system of linear equations.   </strong> A)    B)    C)    D)   E)
E) <strong>Use inverse matrices to solve the system of linear equations.   </strong> A)    B)    C)    D)   E)
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29
Use inverse matrices to solve the system of linear equations.<strong>Use inverse matrices to solve the system of linear equations.  </strong> A)    B)    C)    D)    E)

A) <strong>Use inverse matrices to solve the system of linear equations.  </strong> A)    B)    C)    D)    E)
B) <strong>Use inverse matrices to solve the system of linear equations.  </strong> A)    B)    C)    D)    E)
C) <strong>Use inverse matrices to solve the system of linear equations.  </strong> A)    B)    C)    D)    E)
D) <strong>Use inverse matrices to solve the system of linear equations.  </strong> A)    B)    C)    D)    E)
E) <strong>Use inverse matrices to solve the system of linear equations.  </strong> A)    B)    C)    D)    E)
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30
Use inverse matrices and the graphing calculator to find the solution of the system of equations. <strong>Use inverse matrices and the graphing calculator to find the solution of the system of equations.   </strong> A)    B)    C)    D)    E)

A) <strong>Use inverse matrices and the graphing calculator to find the solution of the system of equations.   </strong> A)    B)    C)    D)    E)
B) <strong>Use inverse matrices and the graphing calculator to find the solution of the system of equations.   </strong> A)    B)    C)    D)    E)
C) <strong>Use inverse matrices and the graphing calculator to find the solution of the system of equations.   </strong> A)    B)    C)    D)    E)
D) <strong>Use inverse matrices and the graphing calculator to find the solution of the system of equations.   </strong> A)    B)    C)    D)    E)
E) <strong>Use inverse matrices and the graphing calculator to find the solution of the system of equations.   </strong> A)    B)    C)    D)    E)
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31
Let <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)    , <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)    . Find an elementary matrix E such that <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)    .

A) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)
B) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)
C) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)
D) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)
E) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)    C)    D)    E)
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32
Let <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)    , <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)    . Find an elementary matrix E such that <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)    .

A) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)
B) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)
C) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)
D) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)
E) <strong>Let   ,   . Find an elementary matrix E such that   .</strong> A)    B)   C)    D)   E)
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33
Find the inverse of the elementary matrix <strong>Find the inverse of the elementary matrix   </strong> A)    B)    C)   D)    E)

A) <strong>Find the inverse of the elementary matrix   </strong> A)    B)    C)   D)    E)
B) <strong>Find the inverse of the elementary matrix   </strong> A)    B)    C)   D)    E)
C) <strong>Find the inverse of the elementary matrix   </strong> A)    B)    C)   D)    E)
D) <strong>Find the inverse of the elementary matrix   </strong> A)    B)    C)   D)    E)
E) <strong>Find the inverse of the elementary matrix   </strong> A)    B)    C)   D)    E)
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34
Find the inverse of the matrix <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)

A) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)
B) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)
C) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)
D) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)
E) <strong>Find the inverse of the matrix   </strong> A)    B)    C)    D)    E)
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35
Find the inverse of the matrix <strong>Find the inverse of the matrix   using elementary matrices.</strong> A)    B)   C)   D)   E)   using elementary matrices.

A)
<strong>Find the inverse of the matrix   using elementary matrices.</strong> A)    B)   C)   D)   E)

B)
<strong>Find the inverse of the matrix   using elementary matrices.</strong> A)    B)   C)   D)   E)
C)
<strong>Find the inverse of the matrix   using elementary matrices.</strong> A)    B)   C)   D)   E)
D)
<strong>Find the inverse of the matrix   using elementary matrices.</strong> A)    B)   C)   D)   E)
E)
<strong>Find the inverse of the matrix   using elementary matrices.</strong> A)    B)   C)   D)   E)
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36
Which of the following is a product of elementary matrices for the matrix <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)    D)   E)

A) <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)    D)   E)
B) <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)    D)   E)
C) <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)    D)   E)
D) <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)    D)   E)
E) <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)    D)   E)
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37
Which of the following is a product of elementary matrices for the matrix <strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)   D)   E)

A)
<strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)   D)   E)
B)
<strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)   D)   E)
C)
<strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)   D)   E)
D)
<strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)   D)   E)
E)
<strong>Which of the following is a product of elementary matrices for the matrix   </strong> A)   B)   C)   D)   E)
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38
Which of the following is the LU-factorization of the matrix <strong>Which of the following is the LU-factorization of the matrix   </strong> A)    B)    C)    D)    E)

A) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)    B)    C)    D)    E)
B) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)    B)    C)    D)    E)
C) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)    B)    C)    D)    E)
D) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)    B)    C)    D)    E)
E) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)    B)    C)    D)    E)
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39
Which of the following is the LU-factorization of the matrix <strong>Which of the following is the LU-factorization of the matrix   </strong> A)   B)    C)   D)    E)

A) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)   B)    C)   D)    E)
B) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)   B)    C)   D)    E)
C) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)   B)    C)   D)    E)
D) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)   B)    C)   D)    E)
E) <strong>Which of the following is the LU-factorization of the matrix   </strong> A)   B)    C)   D)    E)
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40
The market research department at a manufacturing plant determines that 30% of the people who purchase the plant's product during any month will not purchase it the next month. On the other hand, 40% of the people who do not purchase the product during any month will purchase it the next month. In a population of 1000 people, 100 people purchased the product this month. How many will purchase the product next month?

A) 510 people
B) 570 people
C) 430 people
D) 400 people
E) 370 people
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41
The market research department at a manufacturing plant determines that 30% of the people who purchase the plant's product during any month will not purchase it the next month. On the other hand, 60% of the people who do not purchase the product during any month will purchase it the next month. In a population of 1000 people, 200 people purchased the product this month. How many will purchase the product in 2 months?

A) 638 people
B) 830 people
C) 744 people
D) 812 people
E) 662 people
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42
A population of 10,000 is grouped as follows: 5,000 nonsmokers, 3,500 smokers of one pack or less per day, and 1,500 smokers of more than one pack per day. During any month there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 5% probability of quitting and a 20% probability of dropping to a pack or less per day. How many people will be in each of the three groups in 1 month?

A) The number of people in each group is as follows: 5,475 nonsmokers, 3,150 smokers of one pack or less per day, and 1,375 smokers of more than one pack per day.
B) The number of people in each group is as follows: 4,975 nonsmokers, 3,350 smokers of one pack or less per day, and 1,675 smokers of more than one pack per day.
C) The number of people in each group is as follows: 5,475 nonsmokers, 3,350 smokers of one pack or less per day, and 1,175 mokers of more than one pack per day.
D) The number of people in each group is as follows: 4,975 nonsmokers, 3,150 smokers of one pack or less per day, and 1,875 mokers of more than one pack per day.
E) The number of people in each group is as follows: 4,775 nonsmokers, 1,875 smokers of one pack or less per day, and 3,350 smokers of more than one pack per day.
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43
A population of 100,000 consumers is grouped as follows: 20,000 users of Brand A, 30,000 users of Brand B, and 50,000 who use neither brand. During any month a Brand A user has a 20% probability of switching to Brand B and a 10% probability of not using either brand. A Brand B user has a 15% probability of switching to Brand A and a 20% probability of not using either brand. A nonuser has a 20% probability of purchasing Brand A and a 25% probability of purchasing Brand B. How many people will be in each group in 1 month?

A) The number of people in each group is as follows: 30,300 users of Brand A, 36,000 users of Brand B, and 33,700 who use neither brand.
B) The number of people in each group is as follows: 41,700 users of Brand A, 28,500 users of Brand B, and 29,800 who use neither brand.
C) The number of people in each group is as follows: 35,500 users of Brand A, 30,300 users of Brand B, and 34,200 who use neither brand.?
D) The number of people in each group is as follows: 28,500 users of Brand A, 36,000 users of Brand B, and 35,500 who use neither brand.
E) The number of people in each group is as follows: 30,300 users of Brand A, 41,700 users of Brand B, and 28,000 who use neither brand.
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44
Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix <strong>Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix   </strong> A)   B)   C)   D)    E)

A) <strong>Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix   </strong> A)   B)   C)   D)    E)
B) <strong>Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix   </strong> A)   B)   C)   D)    E)
C) <strong>Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix   </strong> A)   B)   C)   D)    E)
D) <strong>Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix   </strong> A)   B)   C)   D)    E)
E) <strong>Find the uncoded row matrices of the size for the message: SELL CONSOLIDATED. Then encode the message using the matrix   </strong> A)   B)   C)   D)    E)
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45
Find <strong>Find   of the matrix   to decode the cryptogram. 11 , 21 , 64 , 112 , 25 , 50 , 29 , 49 , 78 , 136 , 20 , 36 , 76 , 127</strong> A) HAPPY_NEW_YEAR B) MEET_ME_FRIDAY C) MEET_ME_SUNDAY D) MEET_ME_MONDAY E) HAPPY_BIRTHDAY of the matrix <strong>Find   of the matrix   to decode the cryptogram. 11 , 21 , 64 , 112 , 25 , 50 , 29 , 49 , 78 , 136 , 20 , 36 , 76 , 127</strong> A) HAPPY_NEW_YEAR B) MEET_ME_FRIDAY C) MEET_ME_SUNDAY D) MEET_ME_MONDAY E) HAPPY_BIRTHDAY to decode the cryptogram. 11 , 21 , 64 , 112 , 25 , 50 , 29 , 49 , 78 , 136 , 20 , 36 , 76 , 127

A) HAPPY_NEW_YEAR
B) MEET_ME_FRIDAY
C) MEET_ME_SUNDAY
D) MEET_ME_MONDAY
E) HAPPY_BIRTHDAY
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46
A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)    where the external demand is <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)    . Round all the entries of the matrix to two decimal places, where applicable.

A) <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)
B) <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)
C) <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)
D) <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)
E) <strong>A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.</strong> A)   B)    C)    D)    E)
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47
A small community includes a farmer, a baker, and a grocer and has the input-output matrix <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)
and external demand matrix <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)    . Solve for the output matrix X in the equation <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)    .

A) <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)
B) <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)
C) <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)
D) <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)
E) <strong>A small community includes a farmer, a baker, and a grocer and has the input-output matrix   and external demand matrix   . Solve for the output matrix X in the equation   .</strong> A)    B)   C)    D)    E)
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48
Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places <strong>Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places  </strong> A)    B)   C)    D)   E)

A) <strong>Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places  </strong> A)    B)   C)    D)   E)
B) <strong>Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places  </strong> A)    B)   C)    D)   E)
C) <strong>Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places  </strong> A)    B)   C)    D)   E)
D) <strong>Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places  </strong> A)    B)   C)    D)   E)
E) <strong>Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places  </strong> A)    B)   C)    D)   E)
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