Deck 2: Matrix Algebra

Question 1

The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, if the products are
defined.

Answer 1

B

Question 2

The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, if the products are
defined.

Answer 2

A

Question 3

Perform the matrix operation.

Answer 3

C

Question 4

Find the matrix product AB, if it is defined.

Question 5

Perform the matrix operation.

Question 6

Perform the matrix operation.

Question 7

Find the matrix product AB, if it is defined.

Question 8

Perform the matrix operation.

Question 9

Perform the matrix operation.

Question 10

Find the matrix product AB, if it is defined.

Question 11

Find the matrix product AB, if it is defined.

Question 12

Perform the matrix operation.

Question 13

Perform the matrix operation.

Question 14

Find the matrix product AB, if it is defined.

Question 15

Find the matrix product AB, if it is defined.

Question 16

Find the matrix product AB, if it is defined.

Question 17

Perform the matrix operation.

Question 18

Perform the matrix operation.

Question 19

The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, if the products are
defined.

Question 20

Find the matrix product AB, if it is defined.

Question 21

Decide whether or not the matrices are inverses of each other.

Question 22

Decide whether or not the matrices are inverses of each other.

Question 23

Find the inverse of the matrix, if it exists

Question 24

Find the inverse of the matrix, if it exists

Question 25

Find the inverse of the matrix, if it exists

Question 26

Find the inverse of the matrix, if it exists

Question 27

Find the inverse of the matrix, if it exists

Question 28

Find the transpose of the matrix.

Question 29

Find the inverse of the matrix, if it exists

Question 30

Decide whether or not the matrices are inverses of each other.

Question 31

Find the transpose of the matrix.

Question 32

Decide whether or not the matrices are inverses of each other.

Question 33

The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, if the products are
defined.

Question 34

Decide whether or not the matrices are inverses of each other.

Question 35

Decide whether or not the matrices are inverses of each other.

Question 36

Decide whether or not the matrices are inverses of each other.

Question 37

Find the inverse of the matrix, if it exists

Question 38

Decide whether or not the matrices are inverses of each other.

Question 39

Decide whether or not the matrices are inverses of each other.

Question 40

Solve the system by using the inverse of the coefficient matrix.

Question 41

Solve the system by using the inverse of the coefficient matrix.
10x1 - 4x2 = -6 6x1 - x2 = 2

A)(4, 1)
B)(1, 4)
C)(-1, -4)
D)(-4, -1)

Question 42

Find the inverse of the matrix A, if it exists.

Question 43

Solve the system by using the inverse of the coefficient matrix.

Question 44

Solve the system by using the inverse of the coefficient matrix.

Question 45

Identify the indicated submatrix.

Question 46

Find the inverse of the matrix A, if it exists.

Question 47

Solve the system by using the inverse of the coefficient matrix.

Question 48

Find the matrix product AB for the partitioned matrices.

Question 49

Determine whether the matrix is invertible.

Question 50

Find the matrix product AB for the partitioned matrices.

Question 51

Find the inverse of the matrix A, if it exists.

Question 52

Solve the equation Ax = b by using the LU factorization given for A.

Question 53

Find the inverse of the matrix A, if it exists.

Question 54

Find the inverse of the matrix A, if it exists.

Question 55

Solve the system by using the inverse of the coefficient matrix.

Question 56

Find the inverse of the matrix A, if it exists.

Question 57

Identify the indicated submatrix.

Question 58

Solve the system by using the inverse of the coefficient matrix.

Question 59

Solve the system by using the inverse of the coefficient matrix.

Question 60

Determine whether the matrix is invertible.

Question 61

Find an LU factorization of the matrix A.

Question 62

Find the 3 × 3 matrix that produces the described transformation, using homogeneous coordinates.
Reflect through the x-axis

Question 63

Question 64

Determine the production vector x that will satisfy demand in an economy with the given consumption matrix C and
final demand vector d. Round production levels to the nearest whole number.

Question 65

Determine whether b is in the column space of A.

Question 66

Find the 3 × 3 matrix that produces the described composite 2D transformation, using homogeneous coordinates.
Rotate points through 45° and then scale the x-coordinate by 0.6 and the y-coordinate by 0.8.

Question 67

Determine the production vector x that will satisfy demand in an economy with the given consumption matrix C and
final demand vector d. Round production levels to the nearest whole number.

Question 68

Determine the production vector x that will satisfy demand in an economy with the given consumption matrix C and
final demand vector d. Round production levels to the nearest whole number.

Question 69

Find the 4 × 4 matrix that produces the described transformation, using homogeneous coordinates.
Translation by the vector (4, -6, -3)72)

Question 70

Find a basis for the null space of the matrix.

Question 71

Determine whether b is in the column space of A.

Question 72

Find the 3 × 3 matrix that produces the described composite 2D transformation, using homogeneous coordinates.
Translate by (8, 6), and then reflect through the line y = x.

Question 73

Find a basis for the column space of the matrix.

Question 74

Find the 4 × 4 matrix that produces the described transformation, using homogeneous coordinates.
Rotation about the y-axis through an angle of 60° 73)

Question 75

Find a basis for the null space of the matrix.

Question 76

Find the 3 × 3 matrix that produces the described transformation, using homogeneous coordinates.

Question 77

Determine the production vector x that will satisfy demand in an economy with the given consumption matrix C and
final demand vector d. Round production levels to the nearest whole number.

Question 78

Find an LU factorization of the matrix A.

Question 79

Find a basis for the column space of the matrix.

Question 80

Solve the equation Ax = b by using the LU factorization given for A.