Deck 20: Mathematical Tools: Determinants and Matrices

Question 1

An n × m determinant is the same as an n × m matrix.

Answer 1

False

Question 2

We can always perform the matrix multiplication AA.

Answer 2

False

Question 3

An n × m matrix multiplied by a p × m matrix yields an n × p matrix.

Answer 3

False

Question 4

The matrix multiplication (AB), where A and B are any matrix, is equal to the matrix multiplication (BA).

Question 5

An n × m matrix, when added to an m × n matrix (n ≠ m), yields an n × n matrix.

Question 6

A matrix multiplied by its inverse is always equal to the identity matrix.

Question 7

We cannot multiply an n × m matrix by a 1 × m matrix.

Question 8

We can develop an n × m matrix by adding an n × p matrix and an n × r matrix where p + r = m.

Question 9

An identity matrix has 1's in all positions of the matrix.

Question 10

A cofactor of a matrix is the set of numbers that remains after a given row and column have been removed from a matrix.

Question 11

We cannot multiply an n × m matrix by an m × 1 matrix.

Question 12

An adjoint is the transpose of the matrix of cofactors.

Question 13

A matrix having only a single column with multiple rows, or a single row with multiple columns, is called a vector.

Question 14

A^-1A = A A^-1 = I

Question 15

An n × m matrix, when multiplied by an m × n matrix, yields an n × n matrix.

Question 16

We can find only the inverse of square matrices.

Question 17

The subtraction of an n × m matrix from an n × m matrix yields an n × m matrix.

Question 18

Determinants are useful in solving a set of simultaneous equations.

Question 19

A determinant has a single numerical value.

Question 20

We can develop an n × m matrix by the addition of an n × m matrix and an n × p matrix, where p < n.

Question 21

An n × m matrix, when multiplied by an n × m matrix, yields

A)an n × m matrix.
B)an m × n matrix.
C)an n² × m² matrix.
D)These matrices cannot be multiplied.

Question 22

Matrices can be used by television station executives to describe the channel switching behavior of their eight o'clock TV news audience.

Question 23

To create the transpose of a given matrix, we simply interchange the rows with the columns.

Question 24

An n × n matrix, when multiplied by an n × n matrix, yields

A)an n × n matrix.
B)a 2n matrix.
C)an n² + n² matrix.
D)an (n × n)² matrix.

Question 25

× =

Question 26

A set of simultaneous equations can be solved through the use of determinants by setting up a proportion of two special determinants for each unknown variable.

Question 27

= 70

Question 28

An n × m matrix, when multiplied by an m × n matrix, yields

A)an n × m matrix.
B)an m × n matrix.
C)an n × n matrix.
D)an n × m × n matrix.

Question 29

A matrix is

A)a determination of probability.
B)a qualitative tool used to solve a set of simultaneous equations.
C)an array of numbers.
D)a single column of non-zero numbers.

Question 30

Add the matrices +

A)
B)
C)
D)

Question 31

× × =

Question 32

× =

Question 33

The value of the determinant is

A)ab - cd.
B)ac - bd.
C)ab + cd.
D)ad - cb.

Question 34

An n × m matrix, when added to an n × m matrix, yields

A)an n × m matrix.
B)an m × n matrix.
C)a 2(n × m)matrix.
D)a 2n × 2m matrix.

Question 35

As a mathematical tool, determinants are of value in helping to solve a series of simultaneous equations.

Question 36

= 7

Question 37

An n × m matrix, when added to an m × n matrix, yields

A)an n × m matrix.
B)an m × n matrix.
C)a 2(n × m)matrix.
D)These matrices cannot be added.

Question 38

The correct determinant value for the determinant would be

A)(8)(4)(3)(6).
B)(8)(4)+ (3)(6).
C)(8)(4)- (3)(6).
D)(8)(3)- (6)(4).

Question 39

The value of the determinant of is 8.

Question 40

An n × m matrix, when multiplied by an m × p matrix, yields

A)an n × m × m × p matrix.
B)an n × m × p matrix.
C)an n × p matrix.
D)a p matrix.

Question 41

The value of the determinant is

A)128.
B)96.
C)8.
D)232.

Question 42

Element 1,2 of the inverse of the matrix is

A)-5.
B)-4.
C)3.
D)7.

Question 43

Element 1,1 of the inverse of the matrix is

A)-5.
B)-4.
C)3.
D)7.

Question 44

To solve the following set of simultaneous equations, the determinant solution for Y would be 4X + 3Y = 7
2X - 2Y = 5

A)X = ÷

B)X = ÷

C)X = ÷

D)X = ÷

Question 45

Element 1,1 of the inverse of the matrix is

A)-5.
B)-4.
C)4.
D)5.

Question 46

The value of the determinant is

A)-8.
B)+8.
C)-40.
D)+40.

Question 47

The value of the determinant is

A)8.
B)7.
C)4.
D)-4.

Question 48

The value of the determinant is

A)2.
B)14.
C)-42.
D)42.

Question 49

The value of the determinant is

A)30.
B)42.
C)16.
D)20.

Question 50

To solve the following set of simultaneous equations, the determinant solution for X would be 4X + 3Y = 7
2X - 2Y = 5

A)X = ÷

B)X = ÷

C)X = ÷

D)X = ÷

Question 51

Element 2,2 of the inverse of the matrix is

A)-5.
B)-4.
C)3.
D)7.

Question 52

Element 2,1 of the inverse of the matrix is

A)-5.
B)-4.
C)3.
D)7.

Question 53

The value of the determinant is

A)21.
B)50.
C)0.
D)48.

Question 54

The value of the determinant is

A)6243.
B)24.
C)15.
D)10.

Question 55

Add the matrices + .

A)
B)
C)
D)Matrices of these dimensions cannot be added.

Question 56

The value of the determinant is

A)not able to be determined.
B)0.
C)80.
D)-80.

Question 57

An n × m matrix when added to a p × m matrix (p < m), yields

A)an n × m matrix.
B)an n × p matrix.
C)an m × p matrix.
D)Matrices of these dimensions cannot be added.

Question 58

The value of the determinant is

A)60.
B)6.
C)54.
D)21.

Question 59

Multiply matrix by .

A)
B)
C)
D)

Question 60

Multiply matrix by .

A)
B)
C)
D)

Question 61

- =

A)
B)
C)
D)

Question 62

=

A)
B)
C)
D)

Question 63

=

A)
B)
C)
D)

Question 64

=

A)
B)
C)
D)

Question 65

Matrices and determinants are useful for

A)Poisson processes.
B)exponential smoothing.
C)linear programming.
D)finding the roots of equations

Question 66

=

A)
B)
C)
D)

Question 67

=

A)
B)
C)
D)

Question 68

What value for X will result in the value for the determinant to equal -48?

A)0
B)1
C)2
D)3

Question 69

Which one of the following is not a step in computing a matrix of cofactors?

A)selecting an element in the original matrix
B)calculating the value of the determinant of the cofactor
C)returning to step 1 and continue until all elements in the original matrix have been replaced by their cofactor values
D)interchanging the rows with the columns

Question 70

Transpose =

A)
B)
C)
D)

Question 71

Which of the following mathematical operations cannot be performed on matrices?

A)matrix addition, subtraction, and multiplication
B)matrix inversion
C)transposing a matrix
D)multiple regression

Question 72

The correct determinant value for the determinant would be

A)0.
B)48.
C)32.
D)24.

Question 73

=

A)0
B)3
C)-5
D)-3

Question 74

A)11
B)-11
C)15
D)4

Question 75

Evaluate this expression: × =

A)160
B)480
C)240
D)320

Question 76

Which of the following statements is not true about matrix(ces)?

A)A matrix is a display of numbers arranged in rows and columns.
B)Matrices are usually enclosed in parentheses or brackets.
C)Matrices are used as an effective means of presenting or summarizing business data.
D)Matrices cannot be considered as a quantitative tool.

Question 77

The correct determinant value for the determinant would be

A)0.
B)1.
C)-1.
D)-2.

Question 78

=

A)
B)
C)
D)

Question 79

What value for X will result in the value for the determinant to equal 19?

A)9
B)11
C)27
D)13

Question 80

=

A)
B)
C)
D)