Deck 20: Mathematical Tools: Determinants and Matrices

Question 1

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

Answer 1

True

Question 2

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

Answer 2

False

Question 3

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

Answer 3

True

Question 4

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

Question 5

We can always perform the matrix multiplication AA.

Question 6

We can find only the inverse of square matrices.

Question 7

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

Question 8

Determinants are useful in solving a set of simultaneous equations.

Question 9

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

Question 10

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

Question 11

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

Question 12

All matrices have the same number of rows as columns.

Question 13

A determinant has a single numerical value.

Question 14

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

Question 15

An adjoint is the transpose of the matrix of cofactors.

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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

Question 22

[3 2] = [14]

Question 23

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

Question 24

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

Question 25

The value of the determinant of the following matrix is 7.

Question 26

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.
E)None of the above

Question 27

[3 2] = [14]

Question 28

The value of the determinant is

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

Question 29

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)a 2n × 2m matrix.
E)None of the above

Question 30

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)an (n × m)² matrix.
E)None of the above

Question 31

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.
E)None of the above

Question 32

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

Question 33

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).
E)(8)(6)- (3)(4).

Question 34

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

Question 35

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

Question 36

× =

Question 37

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 38

× = [7 7]

Question 39

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

Question 40

The value of the determinant of the following matrix is 7.

Question 41

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.
E)None of the above

Question 42

The value of the determinant is

A)-8.
B)+8.
C)-40.
D)+40.
E)None of the above

Question 43

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 = ÷
E)None of the above

Question 44

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.
E)None of the above

Question 45

Add the matrices +

A)
B)
C)
D)
E)cannot be added

Question 46

The value of the determinant is

A)8.
B)7.
C)4.
D)-4.
E)None of the above

Question 47

Element 1,1 of the inverse of the matrix is

A)-5.
B)-4.
C)4.
D)5.
E)None of the above

Question 48

The value of the determinant is

A)60.
B)6.
C)54.
D)21.
E)None of the above

Question 49

Multiply matrix by .

A)[31 -6]
B)
C)[-6 31]
D)
E)None of the above

Question 50

Element 2,2 of the inverse of the matrix is

A)-5.
B)-4.
C)3.
D)7.
E)None of the above

Question 51

The value of the determinant is

A)128.
B)96.
C)8.
D)232.
E)None of the above

Question 52

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.
E)None of the above

Question 53

The value of the determinant is

A)21.
B)50.
C)0.
D)48.
E)None of the above

Question 54

Element 1,1 of the inverse of the matrix is

A)-5.
B)-4.
C)3.
D)7.
E)None of the above

Question 55

Multiply matrix by .

A)
B)
C)
D)
E)None of the above

Question 56

The value of the determinant is

A)30.
B)42.
C)16.
D)20.
E)None of the above

Question 57

The value of the determinant is

A)6243.
B)24.
C)15.
D)10.
E)None of the above

Question 58

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 = ÷
E)None of the above

Question 59

Element 1,2 of the inverse of the matrix is

A)-5.
B)-4.
C)3.
D)7.
E)None of the above

Question 60

Element 2,1 of the inverse of the matrix is

A)-5.
B)-4.
C)3.
D)7.
E)None of the above

Question 61

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
E)None of the above

Question 62

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
E)None of the above

Question 63

The value of the determinant is

A)2.
B)14.
C)-42.
D)42.
E)None of the above

Question 64

Evaluate the determinant .

Question 65

=

A)
B)
C)
D)
E)None of the above

Question 66

=

A)
B)
C)
D)
E)None of the above

Question 67

Matrices and determinants are useful for

A)Markov analysis.
B)game theory.
C)linear programming.
D)All of the above
E)None of the above

Question 68

The value of the determinant is

A)not able to be determined.
B)0.
C)80.
D)-80.
E)None of the above

Question 69

[1 5] =

A)[35 27]
B)
C)
D)
E)None of the above

Question 70

Evaluate the determinant .

Question 71

=

A)
B)
C)
D)
E)None of the above

Question 72

Transpose =

A)
B)
C)
D)
E)None of the above

Question 73

=

A)11
B)-11
C)15
D)4
E)None of the above

Question 74

[1 5] =

A)
B)
C)[0]
D)[40 26]
E)None of the above

Question 75

=

A)
B)
C)
D)
E)None of the above

Question 76

Add the matrices + .

A)
B)
C)
D)
E)None of the above

Question 77

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)an m × m matrix.
E)None of the above

Question 78

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.
E)None of the above

Question 79

=

A)0
B)3
C)-5
D)-3
E)None of the above

Question 80

- =

A)
B)
C)
D)
E)None of the above