تكلم مع الذكاء الاصطناعي
Deck 4: Matrices
ملء الشاشة (f)
سؤال
Use the following matrices to perform the indicated matrix operations, if possible. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Write the matrix that is the negative of matrix B. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
If matrix M has element 
, what is 
? 
A)
B)
C)
D)
E)
, what is ? A)
B)
C)
D)
E)
سؤال
What is the order of matrices A, B, C, D, E? 
, 
, 
, 
, 
A)Matrix A is 2×2, matrix B is 3×2, matrix C is 2×3, matrix D is 3×3, matrix E is 5×2.
B)Matrix A is 10×5, matrix B is 5×4, matrix C is 3×4, matrix D is 15×3, matrix E is 5×2.
C)Matrix A is 2×2, matrix B is 2×3, matrix C is 3×2, matrix D is 3×3, matrix E is 2×5.
D)Matrix A is 2×2, matrix B is 3×3, matrix C is 3×3, matrix D is 3×3, matrix E is 5×5.
E)Matrix A is 5×2, matrix B is 5×2, matrix C is 3×3, matrix D is 15×3, matrix E is 5×2.
, , , , A)Matrix A is 2×2, matrix B is 3×2, matrix C is 2×3, matrix D is 3×3, matrix E is 5×2.
B)Matrix A is 10×5, matrix B is 5×4, matrix C is 3×4, matrix D is 15×3, matrix E is 5×2.
C)Matrix A is 2×2, matrix B is 2×3, matrix C is 3×2, matrix D is 3×3, matrix E is 2×5.
D)Matrix A is 2×2, matrix B is 3×3, matrix C is 3×3, matrix D is 3×3, matrix E is 5×5.
E)Matrix A is 5×2, matrix B is 5×2, matrix C is 3×3, matrix D is 15×3, matrix E is 5×2.
سؤال
Use the following matrices to perform the indicated matrix operations, if possible. 
; 
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
سؤال
Write a zero matrix that is the same order as D.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the following matrices to perform the indicated matrix operations, if possible.
; 
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
سؤال
Use the following matrices to perform the indicated matrix operations, if possible. 
; 
A)
B)
C)
D)
E)
Is undefined
; A)
B)
C)
D)
E)
Is undefined
سؤال
Write the transpose of matrix F. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the following matrices to perform the indicated matrix operations, if possible. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the following matrices to perform the indicated matrix operations, if possible. 
; 
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
سؤال
Use the following matrices to perform the indicated matrix operations, if possible. 
; 
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
سؤال
Use the following matrices to perform the indicated matrix operations, if possible. 
; 
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
سؤال
What is element 
? 
A)
B)
C)
D)
E)
? A)
B)
C)
D)
E)
سؤال
What is the sum of matrix M and its negative? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the following matrices to perform the indicated matrix operations, if possible. 
; 
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
سؤال
Use the following matrices to perform the indicated matrix operations, if possible. 
; 
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
سؤال
Find x, y, z and w. 
A)
, and
B)
, and
C)
, and
D)
, and
E)
, and
A)
, and
B)
, and
C)
, and
D)
, and
E)
, and
سؤال
Write the transpose of matrix A. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the following matrices to perform the indicated matrix operations, if possible. 
; 
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
سؤال
From the data in the following table, make a matrix A that gives the value (in billions of dollars) of U.S. imports from the various country groupings in the years 2000 and 2002.
Imports to U.S. from Country Groupings
($billions)
Exports from U.S. to Country Groupings
($billions)
A)
B)
C)
D)
E)
Imports to U.S. from Country Groupings
($billions)
Exports from U.S. to Country Groupings($billions)
A)
B)
C)
D)
E)
سؤال
The tables below give the numbers of some species of threatened and endangered wildlife in the United States and in foreign countries in 2003. Let A represent the matrix that contains the number of each of these species in the United States in 2003 and B represent the matrix that contains the number of each of these species outside the United States in 2003. Find the matrix B - A. What do the negative entries in matrix B - A mean?
United States
Foreign 
A)
The negative entries tell us that that particular species is extinct.
B)
The negative entries tell us how many more endangered or threatened species are in foreign countries.
C)
The negative entries tell us that there are more endangered or threatened species in foreign countries.
D)
The negative entries tell us that that particular species is extinct.
E)
The negative entries tell us how many more endangered or threatened species are in the United States.
United States
Foreign A)
The negative entries tell us that that particular species is extinct.
B)
The negative entries tell us how many more endangered or threatened species are in foreign countries.
C)
The negative entries tell us that there are more endangered or threatened species in foreign countries.
D)
The negative entries tell us that that particular species is extinct.
E)
The negative entries tell us how many more endangered or threatened species are in the United States.
سؤال
Using the data in the following tables, Let matrix A represent imports (in billions of dollars) to U.S. from country groupings, and let matrix B represent exports (in billions of dollars) from U.S. to country groupings. Find the U.S. trade balance with each country grouping in each year by finding matrix B - A.
Imports to U.S. from Country Groupings
($billions)
Exports from U.S. to Country Groupings
($billions)
A)
B)
C)
D)
E)
Imports to U.S. from Country Groupings
($billions)
Exports from U.S. to Country Groupings($billions)
A)
B)
C)
D)
E)
سؤال
Using the data in the following tables, Let matrix A represent imports (in billions of dollars) to U.S. from country groupings, and let matrix B represent exports (in billions of dollars) from U.S. to country groupings. Find the total U.S. trade with these groupings by finding A + B. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The tables below give the numbers of some species of threatened and endangered wildlife in the United States and in foreign countries in 2003. Write a matrix A that contains the number of each of these species in the United States in 2003 and a matrix B that contains the number of each of these species outside the United States in 2003.
United States
Foreign 
A)
,
B)
,
C)
,
D)
,
E)
,
United States
Foreign A)
,
B)
,
C)
,
D)
,
E)
,
سؤال
Let matrix A represent the sales (in thousands of dollars) for the Walbash Company in 2004 in various cities, and let matrix B represent the sales (in thousands of dollars) for the same company in 2005 in the same cities. Write the matrix that represents the change in sales by type (wholesale and retail) and city (Chicago, Atlanta, and Memphis) from 2004 to 2005. 
; 
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
سؤال
The tables below give the numbers of some species of threatened and endangered wildlife in the United States and in foreign countries in 2003. Find a matrix with the total number of these species. Assume that U.S. and foreign species are different.
United States
Foreign 
A)
B)
C)
D)
E)
United States
Foreign A)
B)
C)
D)
E)
سؤال
A poll of 3620 people revealed that of the respondents who were registered Republicans, 893 approved of the president's job performance, 257 did not, and 135 had no opinion. Of the registered Democrats, 142 approved of the president's job performance, 426 did not, and 501 had no opinion. Of those registered as Independents, 177 approved, 64 did not approve, and 801 had no opinion. Of the remaining respondents, who were not registered, 142 approved, 38 did not approve, and 44 had no opinion. Represent these data in a 3×4 matrix.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Solve for x, y and z. 
A)
And
B)
And
C)
And
D)
And
E)
And
A)
And
B)
And
C)
And
D)
And
E)
And
سؤال
The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their 2002 data. Which breed had the largest increase in the number of registrations?
1995
2002 
A)
B)
C)
D)
E)
1995
2002 A)
B)
C)
D)
E)
سؤال
Ace, Baker, and Champ are being purchased by ALCO, Inc., and their outstanding debts must be paid by the purchaser. The matrix below gives the amounts of debt and the terms for the companies being purchased. If ALCO pays 35% of the amount owed on each debt, write the matrix giving the remaining debts.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The following tables give the capital expenditures and gross operating costs of manufacturing establishments for pollution abatement, in millions of dollars. Use a calculator or spreadsheet to find the sum of the matrices containing these data. This will yield the total costs of manufacturing establishments for air, water, and solid contained waste pollution abatement for the years 2002-2005.
Pollution Abatement Capital Expenditures
Pollution Abatement Gross Operating Costs 
A)
B)
C)
D)
E)
Pollution Abatement Capital Expenditures
Pollution Abatement Gross Operating Costs A)
B)
C)
D)
E)
سؤال
The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their 2002 data. Form a matrix for the 1995 data and a matrix for the 2002 data.
1995
2002 
A)
;
B)
;
C)
;
D)
;
E)
;
1995
2002 A)
;
B)
;
C)
;
D)
;
E)
;
سؤال
The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their 2002 data. Which breed had the greatest improvement in rank? 1995 
2002 
A)
B)
C)
D)
E)
2002 A)
B)
C)
D)
E)
سؤال
The following tables give the capital expenditures and gross operating costs of manufacturing establishments for pollution abatement, in millions of dollars. Which type of pollution abatement was most expensive in 2005?
Pollution Abatement Capital Expenditures
Pollution Abatement Gross Operating Costs 
A)Solid Contained Waste
B)Water
C)Air
Pollution Abatement Capital Expenditures
Pollution Abatement Gross Operating Costs A)Solid Contained Waste
B)Water
C)Air
سؤال
The following tables give the death rates, per 100,000 population, by age for selected years for males and females. If matrix M gives the male data and matrix F gives the female data, use matrix operations to find the death rate per 100,000 for all people in the age categories given and for the given years.
Males
Females 
A)
B)
C)
D)
E)
Males
Females
A)
B)
C)
D)
E)
سؤال
Find x, y, z, and w . 
A)
And
B)
And
C)
And
D)
And
E)
And
A)
And
B)
And
C)
And
D)
And
E)
And
سؤال
The following tables give the death rates, per 100,000 population, by age for selected years for males and females. If matrix M gives the male data and matrix F gives the female data, find matrix M - F and describe what it means.
Males
Females 
A)
M - F represents how much greater the numbers are for males in each category per year.
B)
M - F represents how much greater the numbers are for males in each category per year.
C)
M - F represents how much greater the numbers are for females in each category per year.
D)
M - F represents how much greater the numbers are for females in each category per year.
E)
M - F represents only the male death rates, per 100,000 population by age.
Males
Females
A)
M - F represents how much greater the numbers are for males in each category per year.
B)
M - F represents how much greater the numbers are for males in each category per year.
C)
M - F represents how much greater the numbers are for females in each category per year.
D)
M - F represents how much greater the numbers are for females in each category per year.
E)
M - F represents only the male death rates, per 100,000 population by age.
سؤال
Find x, y, z and w. 
A)
And
B)
And
C)
And
D)
And
E)
And
A)
And
B)
And
C)
And
D)
And
E)
And
سؤال
Let matrix A represent the sales (in thousands of dollars) for the Walbash Company in 2004 in various cities, and let matrix B represent the sales (in thousands of dollars) for the same company in 2005 in the same cities. Write the matrix that represents the total sales by type (wholesale and retail) and city (Chicago, Atlanta, and Memphis) for both years. 
; 
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
سؤال
In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. 
Construct matrix A with elements 
.
A)
B)
C)
D)
E)
Construct matrix A with elements .
A)
B)
C)
D)
E)
سؤال
Use matrix A to find A2, if possible. 
A)
B)
C)
D)
E)A2 is undefined.
A)
B)
C)
D)
E)A2 is undefined.
سؤال
In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2.
1
2 
5 
3 
4
Construct matrix B with elements
.
A)
B)
C)
D)
E)
1
2 5 3 4Construct matrix B with elements
.
A)
B)
C)
D)
E)
سؤال
Use the matrices to find CD, if possible. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. 
Let matrix A represent the matrix with the following elements: 
.
Let matrix B represent the matrix with the following elements:
.
The player i is the top-ranked player if the sum of row i in the matrix A + B is the largest. What is the number of this player?
A)player 3
B)player 2
C)player 5
D)player 1
E)player 4
Let matrix A represent the matrix with the following elements: .Let matrix B represent the matrix with the following elements:
.The player i is the top-ranked player if the sum of row i in the matrix A + B is the largest. What is the number of this player?
A)player 3
B)player 2
C)player 5
D)player 1
E)player 4
سؤال
Use the matrices to find 
, if possible. 
A)
B)
C)
D)
E)
Is undefined.
, if possible. A)
B)
C)
D)
E)
Is undefined.
سؤال
When a firm buys another company, the company frequently has some outstanding debt that the purchaser must pay. Consider three companies, A, B, and C, that are purchased by Maxx Industries. The following table gives the amount of each company's debt, classified by the number of days remaining until the debt must be paid. Suppose Maxx Industries pays 20% of the amount owed on each loan. Write the matrix that would give the remaining debt in each category. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the matrices to find CF, if possible.
A)
B)
C)
D)
E)CF is undefined.
A)
B)
C)
D)
E)CF is undefined.
سؤال
Multiply the matrices. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the matrices to find BA, if possible.
A)
B)
C)
D)
E)BA is undefined.
A)
B)
C)
D)
E)BA is undefined.
سؤال
Ace, Baker, and Champ are being purchased by ALCO, Inc., and their outstanding debts must be paid by the purchaser. The matrix below gives the amounts of debt and the terms for the companies being purchased. Suppose ALCO decides to pay 80% of all debts due in 30 days and to increase the debts due in 60 days by 20%. Write a matrix that gives the debts after these transactions are made.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the matrices to find DE, if possible.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the matrices to find 
, if possible. 
A)
B)
C)
D)
E)
Is undefined.
, if possible.
A)
B)
C)
D)
E)
Is undefined.
سؤال
The figure that follows depicts the mean (average) flow time for a job when the critical-ratio rule is used to dispatch workers at several machines required to complete the job. In the figure, WHN 1, WHN 2, and WHN 3 represent three different rules for determining when a worker should be transferred to another machine, and Where represents six rules for determining the machine to which the worker is transferred. Construct a 3×6 matrix A to represent these data, with entries rounded to the nearest integer. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the matrices to find BE, if possible. 
A)
B)
C)
D)
E)BE is undefined.
A)
B)
C)
D)
E)BE is undefined.
سؤال
Use the matrices to find EC, if possible.
A)
B)
C)
D)
E)EC is undefined.
A)
B)
C)
D)
E)EC is undefined.
سؤال
Multiply the matrices. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
When a firm buys another company, the company frequently has some outstanding debt that the purchaser must pay. Consider three companies, A, B, and C, that are purchased by Maxx Industries. The following table gives the amount of each company's debt, classified by the number of days remaining until the debt must be paid. What payment plan did Maxx Industries use if the outstanding debt is given by the following matrix? 
A)They paid 30% of the debts due in 30 days, 100% of the debts due in 60 days, and 100% of the debts due in more than 60 days.
B)They paid 30% of the debts due in 30 days, 30% of the debts due in 60 days, and 100% of the debts due in more than 60 days.
C)They paid 100% of the debts due in 30 days, 100% of the debts due in 60 days, and 30% of the debts due in more than 60 days.
D)They paid 100% of the debts due in 30 days, 30% of the debts due in 60 days, and 100% of the debts due in more than 60 days.
E)They paid 100% of the debts due in 30 days, 30% of the debts due in 60 days, and 30% of the debts due in more than 60 days.
A)They paid 30% of the debts due in 30 days, 100% of the debts due in 60 days, and 100% of the debts due in more than 60 days.
B)They paid 30% of the debts due in 30 days, 30% of the debts due in 60 days, and 100% of the debts due in more than 60 days.
C)They paid 100% of the debts due in 30 days, 100% of the debts due in 60 days, and 30% of the debts due in more than 60 days.
D)They paid 100% of the debts due in 30 days, 30% of the debts due in 60 days, and 100% of the debts due in more than 60 days.
E)They paid 100% of the debts due in 30 days, 30% of the debts due in 60 days, and 30% of the debts due in more than 60 days.
سؤال
Multiply the matrices. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use a computer spreadsheet to find the average efficiency for each work center over the first five workers. Which work center is the most efficient? 
A)Number 1
B)Number 4
C)Number 3
D)Number 8
A)Number 1
B)Number 4
C)Number 3
D)Number 8
سؤال
Substitute the given values of x, y, and z into the matrix equation and use matrix multiplication to determine if the values satisfy the equation. 
, 
, 
A)True
B)False
, , A)True
B)False
سؤال
Using the matrices A and B below, what condition must be satisfied in order that AB and BA are defined? 
and 
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
سؤال
Substitute the given values of x, y, and z into the matrix equation and use matrix multiplication to determine if the values satisfy the equation. 
, 
, 
A)True
B)False
, , A)True
B)False
سؤال
Find AB and BA if 
and 
, with 
.
A)
,
B)
,
C)
,
D)
,
E)
,
and , with . A)
,
B)
,
C)
,
D)
,
E)
,
سؤال
Use the matrices below. Perform the indicated operations. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the matrices below. Perform the indicated operations.
AZ
A)
B)
C)
D)
E)
AZ
A)
B)
C)
D)
E)
سؤال
CD = DC. 
A)True
B)False
A)True
B)False
سؤال
Use the matrices below. Perform the indicated operations.
IA
A)
B)
C)
D)
E)
IA
A)
B)
C)
D)
E)
سؤال
For 
, are FFT and FTF defined?
A)Yes
B)No
, are FFT and FTF defined?A)Yes
B)No
سؤال
Use matrix A to find A3, if possible. 
A)
B)
C)
D)
E)A3 is undefined.
A)
B)
C)
D)
E)A3 is undefined.
سؤال
Use the matrices below. Perform the indicated operations. AI
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use matrix F to find F2, if possible. 
A)
B)
C)
D)
E)F2 is undefined.
A)
B)
C)
D)
E)F2 is undefined.
سؤال
For 
, can 
? Explain.
A)No, because
And
Have the same dimensions but different values.
B)Yes, because
and
Have the same dimensions.
C)Yes, because
and
Have the same values.
D)No, because
and
Have different dimensions.
E)Yes, because
and
Have the same dimensions and the same values.
, can ? Explain. A)No, because
And
Have the same dimensions but different values.
B)Yes, because
and
Have the same dimensions.
C)Yes, because
and
Have the same values.
D)No, because
and
Have different dimensions.
E)Yes, because
and
Have the same dimensions and the same values.
سؤال
Use the matrices below. Perform the indicated operations.
BA
A)
B)
C)
D)
E)
BA
A)
B)
C)
D)
E)
سؤال
(CD)·E and C·(DE) are equal. 
A)True
B)False
A)True
B)False
سؤال
For 
, what size is each product FFT and FTF?
A)FFT is 2×2; FTF is 2×2
B)FFT is 2×2; FTF is 4×4
C)FFT is 4×2; FTF is 4×4
D)FFT is 4×4; FTF is 2×2
E)FFT is 2×4; FTF is 4×2
, what size is each product FFT and FTF? A)FFT is 2×2; FTF is 2×2
B)FFT is 2×2; FTF is 4×4
C)FFT is 4×2; FTF is 4×4
D)FFT is 4×4; FTF is 2×2
E)FFT is 2×4; FTF is 4×2
سؤال
سؤال
Use the matrices below. Perform the indicated operations.
I·F·Z
A)
B)
C)
D)
E)
I·F·Z
A)
B)
C)
D)
E)
سؤال
Substitute the given values of x, y, and z into the matrix equation and use matrix multiplication to determine if the values satisfy the equation. 
, 
, 
A)True
B)False
, , A)True
B)False
سؤال
Use the matrices below. Perform the indicated operations.
DC
A)
B)
C)
D)
E)
DC
A)
B)
C)
D)
E)
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العب
ملء الشاشة (f)
Deck 4: Matrices
1
Use the following matrices to perform the indicated matrix operations, if possible.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Write the matrix that is the negative of matrix B.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
If matrix M has element , what is ?
A)
B)
C)
D)
E)
, what is ? A)
B)
C)
D)
E)
4
What is the order of matrices A, B, C, D, E? , , , ,
A)Matrix A is 2×2, matrix B is 3×2, matrix C is 2×3, matrix D is 3×3, matrix E is 5×2.
B)Matrix A is 10×5, matrix B is 5×4, matrix C is 3×4, matrix D is 15×3, matrix E is 5×2.
C)Matrix A is 2×2, matrix B is 2×3, matrix C is 3×2, matrix D is 3×3, matrix E is 2×5.
D)Matrix A is 2×2, matrix B is 3×3, matrix C is 3×3, matrix D is 3×3, matrix E is 5×5.
E)Matrix A is 5×2, matrix B is 5×2, matrix C is 3×3, matrix D is 15×3, matrix E is 5×2.
, , , , A)Matrix A is 2×2, matrix B is 3×2, matrix C is 2×3, matrix D is 3×3, matrix E is 5×2.
B)Matrix A is 10×5, matrix B is 5×4, matrix C is 3×4, matrix D is 15×3, matrix E is 5×2.
C)Matrix A is 2×2, matrix B is 2×3, matrix C is 3×2, matrix D is 3×3, matrix E is 2×5.
D)Matrix A is 2×2, matrix B is 3×3, matrix C is 3×3, matrix D is 3×3, matrix E is 5×5.
E)Matrix A is 5×2, matrix B is 5×2, matrix C is 3×3, matrix D is 15×3, matrix E is 5×2.
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5
Use the following matrices to perform the indicated matrix operations, if possible. ;
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
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6
Write a zero matrix that is the same order as D.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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7
Use the following matrices to perform the indicated matrix operations, if possible.
;
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
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8
Use the following matrices to perform the indicated matrix operations, if possible. ;
A)
B)
C)
D)
E)
Is undefined
; A)
B)
C)
D)
E)
Is undefined
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9
Write the transpose of matrix F.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Use the following matrices to perform the indicated matrix operations, if possible.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
Use the following matrices to perform the indicated matrix operations, if possible. ;
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
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12
Use the following matrices to perform the indicated matrix operations, if possible. ;
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
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13
Use the following matrices to perform the indicated matrix operations, if possible. ;
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
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14
What is element ?
A)
B)
C)
D)
E)
? A)
B)
C)
D)
E)
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15
What is the sum of matrix M and its negative?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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16
Use the following matrices to perform the indicated matrix operations, if possible. ;
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
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17
Use the following matrices to perform the indicated matrix operations, if possible. ;
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
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18
Find x, y, z and w.
A)
, and
B)
, and
C)
, and
D)
, and
E)
, and
A)
, and
B)
, and
C)
, and
D)
, and
E)
, and
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19
Write the transpose of matrix A.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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20
Use the following matrices to perform the indicated matrix operations, if possible. ;
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
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21
From the data in the following table, make a matrix A that gives the value (in billions of dollars) of U.S. imports from the various country groupings in the years 2000 and 2002.
Imports to U.S. from Country Groupings
($billions) Exports from U.S. to Country Groupings
($billions)
A)
B)
C)
D)
E)
Imports to U.S. from Country Groupings
($billions)
Exports from U.S. to Country Groupings($billions)
A)
B)
C)
D)
E)
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22
The tables below give the numbers of some species of threatened and endangered wildlife in the United States and in foreign countries in 2003. Let A represent the matrix that contains the number of each of these species in the United States in 2003 and B represent the matrix that contains the number of each of these species outside the United States in 2003. Find the matrix B - A. What do the negative entries in matrix B - A mean?
United States Foreign
A)
The negative entries tell us that that particular species is extinct.
B)
The negative entries tell us how many more endangered or threatened species are in foreign countries.
C)
The negative entries tell us that there are more endangered or threatened species in foreign countries.
D)
The negative entries tell us that that particular species is extinct.
E)
The negative entries tell us how many more endangered or threatened species are in the United States.
United States
Foreign A)
The negative entries tell us that that particular species is extinct.
B)
The negative entries tell us how many more endangered or threatened species are in foreign countries.
C)
The negative entries tell us that there are more endangered or threatened species in foreign countries.
D)
The negative entries tell us that that particular species is extinct.
E)
The negative entries tell us how many more endangered or threatened species are in the United States.
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23
Using the data in the following tables, Let matrix A represent imports (in billions of dollars) to U.S. from country groupings, and let matrix B represent exports (in billions of dollars) from U.S. to country groupings. Find the U.S. trade balance with each country grouping in each year by finding matrix B - A.
Imports to U.S. from Country Groupings
($billions) Exports from U.S. to Country Groupings
($billions)
A)
B)
C)
D)
E)
Imports to U.S. from Country Groupings
($billions)
Exports from U.S. to Country Groupings($billions)
A)
B)
C)
D)
E)
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24
Using the data in the following tables, Let matrix A represent imports (in billions of dollars) to U.S. from country groupings, and let matrix B represent exports (in billions of dollars) from U.S. to country groupings. Find the total U.S. trade with these groupings by finding A + B.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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25
The tables below give the numbers of some species of threatened and endangered wildlife in the United States and in foreign countries in 2003. Write a matrix A that contains the number of each of these species in the United States in 2003 and a matrix B that contains the number of each of these species outside the United States in 2003.
United States Foreign
A)
,
B)
,
C)
,
D)
,
E)
,
United States
Foreign A)
,
B)
,
C)
,
D)
,
E)
,
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26
Let matrix A represent the sales (in thousands of dollars) for the Walbash Company in 2004 in various cities, and let matrix B represent the sales (in thousands of dollars) for the same company in 2005 in the same cities. Write the matrix that represents the change in sales by type (wholesale and retail) and city (Chicago, Atlanta, and Memphis) from 2004 to 2005. ;
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
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27
The tables below give the numbers of some species of threatened and endangered wildlife in the United States and in foreign countries in 2003. Find a matrix with the total number of these species. Assume that U.S. and foreign species are different.
United States Foreign
A)
B)
C)
D)
E)
United States
Foreign A)
B)
C)
D)
E)
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28
A poll of 3620 people revealed that of the respondents who were registered Republicans, 893 approved of the president's job performance, 257 did not, and 135 had no opinion. Of the registered Democrats, 142 approved of the president's job performance, 426 did not, and 501 had no opinion. Of those registered as Independents, 177 approved, 64 did not approve, and 801 had no opinion. Of the remaining respondents, who were not registered, 142 approved, 38 did not approve, and 44 had no opinion. Represent these data in a 3×4 matrix.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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29
Solve for x, y and z.
A)
And
B)
And
C)
And
D)
And
E)
And
A)
And
B)
And
C)
And
D)
And
E)
And
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30
The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their 2002 data. Which breed had the largest increase in the number of registrations?
1995 2002
A)
B)
C)
D)
E)
1995
2002 A)
B)
C)
D)
E)
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31
Ace, Baker, and Champ are being purchased by ALCO, Inc., and their outstanding debts must be paid by the purchaser. The matrix below gives the amounts of debt and the terms for the companies being purchased. If ALCO pays 35% of the amount owed on each debt, write the matrix giving the remaining debts.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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32
The following tables give the capital expenditures and gross operating costs of manufacturing establishments for pollution abatement, in millions of dollars. Use a calculator or spreadsheet to find the sum of the matrices containing these data. This will yield the total costs of manufacturing establishments for air, water, and solid contained waste pollution abatement for the years 2002-2005.
Pollution Abatement Capital Expenditures Pollution Abatement Gross Operating Costs
A)
B)
C)
D)
E)
Pollution Abatement Capital Expenditures
Pollution Abatement Gross Operating Costs A)
B)
C)
D)
E)
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33
The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their 2002 data. Form a matrix for the 1995 data and a matrix for the 2002 data.
1995 2002
A)
;
B)
;
C)
;
D)
;
E)
;
1995
2002 A)
;
B)
;
C)
;
D)
;
E)
;
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34
The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their 2002 data. Which breed had the greatest improvement in rank? 1995 2002
A)
B)
C)
D)
E)
2002 A)
B)
C)
D)
E)
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35
The following tables give the capital expenditures and gross operating costs of manufacturing establishments for pollution abatement, in millions of dollars. Which type of pollution abatement was most expensive in 2005?
Pollution Abatement Capital Expenditures Pollution Abatement Gross Operating Costs
A)Solid Contained Waste
B)Water
C)Air
Pollution Abatement Capital Expenditures
Pollution Abatement Gross Operating Costs A)Solid Contained Waste
B)Water
C)Air
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36
The following tables give the death rates, per 100,000 population, by age for selected years for males and females. If matrix M gives the male data and matrix F gives the female data, use matrix operations to find the death rate per 100,000 for all people in the age categories given and for the given years.
Males Females
A)
B)
C)
D)
E)
Males
Females
A)
B)
C)
D)
E)
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37
Find x, y, z, and w .
A)
And
B)
And
C)
And
D)
And
E)
And
A)
And
B)
And
C)
And
D)
And
E)
And
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38
The following tables give the death rates, per 100,000 population, by age for selected years for males and females. If matrix M gives the male data and matrix F gives the female data, find matrix M - F and describe what it means.
Males Females
A)
M - F represents how much greater the numbers are for males in each category per year.
B)
M - F represents how much greater the numbers are for males in each category per year.
C)
M - F represents how much greater the numbers are for females in each category per year.
D)
M - F represents how much greater the numbers are for females in each category per year.
E)
M - F represents only the male death rates, per 100,000 population by age.
Males
Females
A)
M - F represents how much greater the numbers are for males in each category per year.
B)
M - F represents how much greater the numbers are for males in each category per year.
C)
M - F represents how much greater the numbers are for females in each category per year.
D)
M - F represents how much greater the numbers are for females in each category per year.
E)
M - F represents only the male death rates, per 100,000 population by age.
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39
Find x, y, z and w.
A)
And
B)
And
C)
And
D)
And
E)
And
A)
And
B)
And
C)
And
D)
And
E)
And
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40
Let matrix A represent the sales (in thousands of dollars) for the Walbash Company in 2004 in various cities, and let matrix B represent the sales (in thousands of dollars) for the same company in 2005 in the same cities. Write the matrix that represents the total sales by type (wholesale and retail) and city (Chicago, Atlanta, and Memphis) for both years. ;
A)
B)
C)
D)
E)
; A)
B)
C)
D)
E)
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41
In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. Construct matrix A with elements .
A)
B)
C)
D)
E)
Construct matrix A with elements .
A)
B)
C)
D)
E)
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42
Use matrix A to find A2, if possible.
A)
B)
C)
D)
E)A2 is undefined.
A)
B)
C)
D)
E)A2 is undefined.
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43
In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2.
1 2 5 3 4
Construct matrix B with elements .
A)
B)
C)
D)
E)
1
2 5 3 4Construct matrix B with elements
.
A)
B)
C)
D)
E)
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44
Use the matrices to find CD, if possible.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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45
In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. Let matrix A represent the matrix with the following elements: .
Let matrix B represent the matrix with the following elements: .
The player i is the top-ranked player if the sum of row i in the matrix A + B is the largest. What is the number of this player?
A)player 3
B)player 2
C)player 5
D)player 1
E)player 4
Let matrix A represent the matrix with the following elements: .Let matrix B represent the matrix with the following elements:
.The player i is the top-ranked player if the sum of row i in the matrix A + B is the largest. What is the number of this player?
A)player 3
B)player 2
C)player 5
D)player 1
E)player 4
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46
Use the matrices to find , if possible.
A)
B)
C)
D)
E)
Is undefined.
, if possible. A)
B)
C)
D)
E)
Is undefined.
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47
When a firm buys another company, the company frequently has some outstanding debt that the purchaser must pay. Consider three companies, A, B, and C, that are purchased by Maxx Industries. The following table gives the amount of each company's debt, classified by the number of days remaining until the debt must be paid. Suppose Maxx Industries pays 20% of the amount owed on each loan. Write the matrix that would give the remaining debt in each category.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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48
Use the matrices to find CF, if possible.
A)
B)
C)
D)
E)CF is undefined.
A)
B)
C)
D)
E)CF is undefined.
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49
Multiply the matrices.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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50
Use the matrices to find BA, if possible.
A)
B)
C)
D)
E)BA is undefined.
A)
B)
C)
D)
E)BA is undefined.
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51
Ace, Baker, and Champ are being purchased by ALCO, Inc., and their outstanding debts must be paid by the purchaser. The matrix below gives the amounts of debt and the terms for the companies being purchased. Suppose ALCO decides to pay 80% of all debts due in 30 days and to increase the debts due in 60 days by 20%. Write a matrix that gives the debts after these transactions are made.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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52
Use the matrices to find DE, if possible.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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53
Use the matrices to find , if possible.
A)
B)
C)
D)
E)
Is undefined.
, if possible.
A)
B)
C)
D)
E)
Is undefined.
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54
The figure that follows depicts the mean (average) flow time for a job when the critical-ratio rule is used to dispatch workers at several machines required to complete the job. In the figure, WHN 1, WHN 2, and WHN 3 represent three different rules for determining when a worker should be transferred to another machine, and Where represents six rules for determining the machine to which the worker is transferred. Construct a 3×6 matrix A to represent these data, with entries rounded to the nearest integer.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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55
Use the matrices to find BE, if possible.
A)
B)
C)
D)
E)BE is undefined.
A)
B)
C)
D)
E)BE is undefined.
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56
Use the matrices to find EC, if possible.
A)
B)
C)
D)
E)EC is undefined.
A)
B)
C)
D)
E)EC is undefined.
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57
Multiply the matrices.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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58
When a firm buys another company, the company frequently has some outstanding debt that the purchaser must pay. Consider three companies, A, B, and C, that are purchased by Maxx Industries. The following table gives the amount of each company's debt, classified by the number of days remaining until the debt must be paid. What payment plan did Maxx Industries use if the outstanding debt is given by the following matrix?
A)They paid 30% of the debts due in 30 days, 100% of the debts due in 60 days, and 100% of the debts due in more than 60 days.
B)They paid 30% of the debts due in 30 days, 30% of the debts due in 60 days, and 100% of the debts due in more than 60 days.
C)They paid 100% of the debts due in 30 days, 100% of the debts due in 60 days, and 30% of the debts due in more than 60 days.
D)They paid 100% of the debts due in 30 days, 30% of the debts due in 60 days, and 100% of the debts due in more than 60 days.
E)They paid 100% of the debts due in 30 days, 30% of the debts due in 60 days, and 30% of the debts due in more than 60 days.
A)They paid 30% of the debts due in 30 days, 100% of the debts due in 60 days, and 100% of the debts due in more than 60 days.
B)They paid 30% of the debts due in 30 days, 30% of the debts due in 60 days, and 100% of the debts due in more than 60 days.
C)They paid 100% of the debts due in 30 days, 100% of the debts due in 60 days, and 30% of the debts due in more than 60 days.
D)They paid 100% of the debts due in 30 days, 30% of the debts due in 60 days, and 100% of the debts due in more than 60 days.
E)They paid 100% of the debts due in 30 days, 30% of the debts due in 60 days, and 30% of the debts due in more than 60 days.
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59
Multiply the matrices.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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60
Use a computer spreadsheet to find the average efficiency for each work center over the first five workers. Which work center is the most efficient?
A)Number 1
B)Number 4
C)Number 3
D)Number 8
A)Number 1
B)Number 4
C)Number 3
D)Number 8
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61
Substitute the given values of x, y, and z into the matrix equation and use matrix multiplication to determine if the values satisfy the equation. , ,
A)True
B)False
, , A)True
B)False
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62
Using the matrices A and B below, what condition must be satisfied in order that AB and BA are defined? and
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
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63
Substitute the given values of x, y, and z into the matrix equation and use matrix multiplication to determine if the values satisfy the equation. , ,
A)True
B)False
, , A)True
B)False
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64
Find AB and BA if and , with .
A)
,
B)
,
C)
,
D)
,
E)
,
and , with . A)
,
B)
,
C)
,
D)
,
E)
,
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65
Use the matrices below. Perform the indicated operations.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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66
Use the matrices below. Perform the indicated operations.
AZ
A)
B)
C)
D)
E)
AZ
A)
B)
C)
D)
E)
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67
CD = DC.
A)True
B)False
A)True
B)False
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68
Use the matrices below. Perform the indicated operations.
IA
A)
B)
C)
D)
E)
IA
A)
B)
C)
D)
E)
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69
For , are FFT and FTF defined?
A)Yes
B)No
, are FFT and FTF defined?A)Yes
B)No
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70
Use matrix A to find A3, if possible.
A)
B)
C)
D)
E)A3 is undefined.
A)
B)
C)
D)
E)A3 is undefined.
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71
Use the matrices below. Perform the indicated operations. AI
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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72
Use matrix F to find F2, if possible.
A)
B)
C)
D)
E)F2 is undefined.
A)
B)
C)
D)
E)F2 is undefined.
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73
For , can ? Explain.
A)No, because
And
Have the same dimensions but different values.
B)Yes, because
and
Have the same dimensions.
C)Yes, because
and
Have the same values.
D)No, because
and
Have different dimensions.
E)Yes, because
and
Have the same dimensions and the same values.
, can ? Explain. A)No, because
And
Have the same dimensions but different values.
B)Yes, because
and
Have the same dimensions.
C)Yes, because
and
Have the same values.
D)No, because
and
Have different dimensions.
E)Yes, because
and
Have the same dimensions and the same values.
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74
Use the matrices below. Perform the indicated operations.
BA
A)
B)
C)
D)
E)
BA
A)
B)
C)
D)
E)
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75
(CD)·E and C·(DE) are equal.
A)True
B)False
A)True
B)False
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76
For , what size is each product FFT and FTF?
A)FFT is 2×2; FTF is 2×2
B)FFT is 2×2; FTF is 4×4
C)FFT is 4×2; FTF is 4×4
D)FFT is 4×4; FTF is 2×2
E)FFT is 2×4; FTF is 4×2
, what size is each product FFT and FTF? A)FFT is 2×2; FTF is 2×2
B)FFT is 2×2; FTF is 4×4
C)FFT is 4×2; FTF is 4×4
D)FFT is 4×4; FTF is 2×2
E)FFT is 2×4; FTF is 4×2
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77
Is it true for matrices (as it is for real numbers) that multiplication by a zero matrix only sometimes gives is a result of a zero matrix provided the multiplication is defined?
A)True
B)False
A)True
B)False
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78
Use the matrices below. Perform the indicated operations.
I·F·Z
A)
B)
C)
D)
E)
I·F·Z
A)
B)
C)
D)
E)
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79
Substitute the given values of x, y, and z into the matrix equation and use matrix multiplication to determine if the values satisfy the equation. , ,
A)True
B)False
, , A)True
B)False
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80
Use the matrices below. Perform the indicated operations.
DC
A)
B)
C)
D)
E)
DC
A)
B)
C)
D)
E)
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