Deck 9: Matrices and Determinants

Question 1

Determine the size of the matrix.
[6]

A) 1
B) 0 × 0
C) 0
D) 1 × 1

Answer 1

1 × 1

Question 2

Write a system of equations associated with the augmented matrix. Do not try to solve.

A)
B)
C) 4x - 4y = -82x - 3y = 7
D) -4x + 4y = -82x - 3y = 7

Answer 2

4x - 4y = -82x - 3y = 7

Question 3

Write the augmented matrix for the system.

A)
B)
C)
D)

Answer 3

Question 4

Write the augmented matrix for the system.

A)
B)
C)
D)

Question 5

Determine the size of the matrix.

A) 4 × 2
B) 2 × 3
C) 2 × 4
D) 3 × 2

Question 6

Write the augmented matrix for the system.

A)
B)
C)
D)

Question 7

Write a system of equations associated with the augmented matrix. Do not try to solve.

A) x = -8y = 6z = 1
B) x = 0y = -2z = -7
C) x = -9y = 5z = 0
D) x = 8y = -6z = -1

Question 8

Write the augmented matrix for the system.

A)
B)
C)
D)

Question 9

Write the augmented matrix for the system.

A)
B)
C)
D)

Question 10

Write the augmented matrix for the system.

A)
B)
C)
D)

Question 11

Determine the size of the matrix.

A) 6 × 6
B) 2 × 3
C) 3 × 3
D) 9

Question 12

Determine the size of the matrix.

A) 4
B) 2 × 2
C) 2
D) 1

Question 13

Write the augmented matrix for the system.

A)
B)
C)
D)

Question 14

Determine the size of the matrix.

A) 1
B) 3
C) 1 × 3
D) 3 × 1

Question 15

Determine the size of the matrix.

A) 6
B) 3 × 2
C) 2 × 3
D) 3

Question 16

Write a system of equations associated with the augmented matrix. Do not try to solve.

A)
B)
C)
D)

Question 17

Write a system of equations associated with the augmented matrix. Do not try to solve.

A)
B)
C)
D)

Question 18

Write the augmented matrix for the system.

A)
B)
C)
D)

Question 19

Determine the size of the matrix.

A) 8
B) 2 × 4
C) 2
D) 4 × 2

Question 20

Determine the size of the matrix.
[3 -6 7 7]

A) 1
B) 4
C) 4 × 1
D) 1 × 4

Question 21

Determine the row operation that was used on the first matrix to obtain the second matrix.

Question 22

Solve the system using Gaussian elimination.
7x - 5y + 2z = -6 2x + 2y - 9z = 4
35x - 25y + 10z = 5

A) {(-6, 4, 5)}
B) {(x, y, z) 7x - 5y + 2z = 10}
C) {(5, 5, -1)}
D)

Question 23

Solve the system using Gaussian elimination.
4x + 4y = -4 2x - 2y = -10

A) {(2, -3)}
B)
C) {(-3, 2)}
D) {(-3, -2)}

Question 24

Determine the row operation that was used on the first matrix to obtain the second matrix.

Question 25

Determine the row operation that was used on the first matrix to obtain the second matrix.

Question 26

Solve the system using Gaussian elimination.
-3x - y - 9z = -67 6x + 8y - 3z = 50
2x - 5y + z = -25

A) {(2, 7, 6)}
B) {(-2, 7, 4)}
C) {(2, 6, 7)}
D)

Question 27

Determine the row operation that was used on the first matrix to obtain the second matrix.

Question 28

Determine the row operation that was used on the first matrix to obtain the second matrix.

Question 29

Determine the row operation that was used on the first matrix to obtain the second matrix.

Question 30

Solve the system using Gaussian elimination.
-4x - 8y = 2 -20x - 40y = 9

A)
B) {(5, 5)}
C) {(2, 9)}
D) {(x, y) -4x - 8y = 2}

Question 31

Solve the system using Gaussian elimination.

A) {(6, 7, 8)}
B) {(6, 8, 7)}
C) {(-6, 8, 12)}
D)

Question 32

Solve the system using Gaussian elimination.
8x + 6y - z = 87 x - 3y + 3z = -6
-7x + y + z = -32

A) {(6, 3, 7)}
B) {(6, 7, 3)}
C)
D) {(-6, 7, 12)}

Question 33

Perform the indicated row operation on the given augmented matrix.

A)
B)
C)
D)

Question 34

Determine the row operation that was used on the first matrix to obtain the second matrix.

Question 35

Determine the row operation that was used on the first matrix to obtain the second matrix.

Question 36

Determine the row operation that was used on the first matrix to obtain the second matrix.

Question 37

Determine the row operation that was used on the first matrix to obtain the second matrix.

Question 38

Solve the system using Gaussian elimination.
6x + y = 25 6x + 3y = 15

A) {(-5, 5)}
B) {(-5, -5)}
C)
D) {(5, -5)}

Question 39

Perform the indicated row operation on the given augmented matrix.

A)
B)
C)
D)

Question 40

Solve the system using Gaussian elimination.

A) {(-2, -2)}
B) {(-2, 2)}
C)
D) {(2, -2)}

Question 41

Find the values that make the equation true.

A) m = 5, x = 7, n = 4, y = -5, p = 1
B) m = 4, x = 2, n = 5, y = -5, p = 1
C) m = 5, x = 7, n = 2, y = -5, p = 1
D) m = 5, x = 2, n = 4, y = -5, p = 1

Question 42

Solve the system using Gaussian elimination.

A) {(0, 6, -6, 5)}
B) {(1 + w, 4 - 2w, -2 + 2w, w )|w is any real number}
C) {(1, 4, -2, 3)}
D) {(14, 12, -7, -3)}

Question 43

Find the values that make the equation true.

A) a = -6, b = -13, c = 1, d = 10, e = -15, f = 2
B)
C) a = 4, b = 1, c = -1, d = 4, e = 15, f = 0
D) a = 6, b = 13, c = -5, d = -10, e = -3, f = -2

Question 44

Find the sum, if possible.

A)
B)
C)
D)

Question 45

Find the sum, if possible.

A)
B)
C)
D)

Question 46

Solve the system using Gaussian elimination.
8x - 6y + 3z = 44 -40x + 30y - 15z = -220
40x - 30y + 15z = 220

A) {(x, y, z) 40x - 30y + 15z = 44}
B) {(7, 6, 8)}
C)
D) {(x, y, z) 8x - 6y + 3z = 44}

Question 47

Find the sum, if possible.

A)
B)
C) Not defined
D)

Question 48

Find the values that make the equation true.

A) a = 7, x = 2
B) a = 2, x = 7
C) a = 2, x = 2
D) a = 7, x = 7

Question 49

Find the values that make the equation true.

A) x = -5; y = -9; z = -2
B) x = -5; y = 2; z = 9
C) x = 9; y = 2; z = 5
D) x = 5; y = 9; z = 2

Question 50

Find the values that make the equation true.

A) x = 8; y = 0; k = -1
B) x = 5; y = -1; k = 8
C) x = -5; y = 4; k = 1
D) x = 5; y = -4; k = -1

Question 51

Find the values that make the equation true.

A) a = 0; b = 0; q = 0
B) a = -5; b = 4; q = 0
C) a = -4; b = 5; q = 0
D) a = 5; b = -4; q = 0

Question 52

Find the values that make the equation true.

A) m = 0; n = 10; x = 0
B) m = 6; n = 4; x = 2
C) m = -10; n = 0; x = -2
D) m = 10; n = 0; x = 2

Question 53

Find the values that make the equation true.

A) x = 9; y = 1; m = -9
B) x = -1; y = 9; m = 9
C) x = 1; y = 9; m = -9
D) x = -1; y = -9; m = 9

Question 54

Solve the problem.
Ellen wishes to mix candy worth $1.84 per pound with candy worth $8.17 per pound to form 11 pounds of a mixture worth $4.72 per pound. How many pounds of the more expensive candy should she use?

A) 10 pounds
B) 8 pounds
C) 6 pounds
D) 5 pounds

Question 55

Solve the problem.
Anne and Nancy use a metal alloy that is 19% copper to make jewelry. How many ounces of a 10% alloy must be mixed with a 27% alloy to form 119 ounces of the desired alloy?

A) 68 ounces
B) 56 ounces
C) 63 ounces
D) 58 ounces

Question 56

Find the values that make the equation true.
[7 b 5] + [a 8 c] = [3 8 -7]

A) a = 10, b = 16, c = -2
B) a = -4, b = 0, c = -12
C)
D) a = 4, b = 0, c = 12

Question 57

Find the values that make the equation true.
6 p+3 q-7 = k+2 5 -9

A) k = -4; p = -2; q = 2;
B) k = 4; p = 2; q = -2
C) k = 5; p = -2; q = 0
D) k = 2; p = 6; q = -9

Question 58

Solve the problem.
A basketball fieldhouse seats 15,000. Courtside seats sell for $9, end zone for $6, and balcony for $5. Total for a sell-out is $89,000. If half the courtside and balcony and all end zone seats are sold, ticket sales total $50,500.
How many of each type of seat are there?

A) 3000 courtside2000 end zone10,000 balcony
B) 3000 courtside2000 end zone8000 balcony
C) 4000 courtside3000 end zone8000 balcony
D) 3200 courtside1800 end zone10,000 balcony

Question 59

Solve the problem.
A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. They used 95 black, 100 white and 80 red wires. How
Many of each cable were made?

A) 20 cable A15 cable B15 cable C
B) 15 cable A20 cable B15 cable C
C) 48 cable A20 cable B12 cable C
D) 15 cable A16 cable B15 cable C

Question 60

Solve the system using Gaussian elimination.
x + y + 6z = 3 2x + y + 10z = 12

A) {(-4z + 9, -2z - 6, z) z is any real number}
B) {(9, -6, 0)}
C) {(4z + 9, 2z - 6, z) z is any real number}
D)

Question 61

Perform the indicated operation, if possible.

A)
B)
C)
D)

Question 62

Solve the problem.
When the owner of a picture framing store took inventory of her unused frames, she found that she had 45 oak-8", 14 oak-12", 47 oak-18", 11 walnut-8", and 10 walnut-18". Write this information as a 2 x 3 matrix.

A)
B)
C)
D)

Question 63

For the given matrix A, find -A.

A)
B)
C)
D)

Question 64

Solve the system of equations corresponding to the given matrix equation.

A) {(-2, 7, 3)}
B) {(-7, 2, -3)}
C) {(7, -2, 3)}
D) {(0, 2, -3)}

Question 65

For the given matrix A, find -A.

A)
B)
C)
D)

Question 66

Perform the indicated operation, if possible.

A)
B)
C)
D)

Question 67

Find the indicated matrix.
Let A = [-4 2] and B = [1 0]. Find 3A + 4B.

A) [-7 4]
B) [-1 2]
C) [-12 4]
D) [-8 6]

Question 68

Perform the indicated operation, if possible.

A)
B)
C)
D)

Question 69

Find the indicated matrix.
Find 4A.

A)
B)
C)
D)

Question 70

Solve the system of equations corresponding to the given matrix equation.

A) {(4, -9)}
B) {(0, 0)}
C) {(-9, 4)}
D) {(-18, 8)}

Question 71

Find the indicated matrix.
Let B = [-1 4 4 -3]. Find -2B.

A) [2 -8 -8 6]
B) [-3 2 2 -5]
C) [-2 8 8 -6]
D) [2 4 4 -3]

Question 72

Perform the indicated operation, if possible.
[-3 8 2] - [4 3]

A) Not defined
B) [-7 8 -1]
C) [-7 5 -1]
D) [-7 5 2]

Question 73

Perform the indicated operation, if possible.

A) 10 6 -8
B)
C)
D)

Question 74

Find the indicated matrix.
Find C - 4D.

A)
B)
C)
D)

Question 75

Perform the indicated operation, if possible.

A)
B)
C)
D)

Question 76

Find the indicated matrix.
Find 3A + B.

A)
B)
C)
D)

Question 77

Find the indicated matrix.

A)
B)
C)
D)

Question 78

Find the sum, if possible.

A)
B)
C)
D)

Question 79

Perform the indicated operation, if possible.

A)
B)
C)
D)

Question 80

Perform the indicated operation, if possible.

A)
B)
C)
D)