AnswersPrecalculusMatrices and Row Operations

Matrices and Row Operations — Unit test Answers

15 verified answers
1
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The matrix below represents a system of equations.Which of the following describes the solution to this system of equations?

Question illustration
A
dependent
B
inconsistent
C
independent
D
unique
2
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Given matrices G and H below, which statement is true?

Question illustration
A
Matrices G and H are not inverses of each other because G + H I.
Option A
B
Matrices G and H are not inverses of each other because GH I.
Option B
C
Matrices G and H are inverses of each other because GH = I.
D
Matrices G and H are inverses of each other because G + H = I.
3

What are the values of x and y in the matrix equation below?

Question illustration
A
mc026-2.jpg
Option A
B
mc026-3.jpg
Option B
C
mc026-4.jpg
Option C
D
mc026-5.jpg
Option D
4

James bought two shirts and three pairs of pants for $87. Matthew bought two pairs of pants and one shirt for $53. Assuming each pair of pants costs the same amount and each shirt costs the same amount, how much does one pair of pants cost?

A
mc023-1.jpg
Option A
B
mc023-2.jpg
Option B
C
mc023-3.jpg
Option C
D
mc023-4.jpg
Option D
5

Which determinants can be used to solve for x and y in the system of linear equations below?

Question illustration
A
, ,
Option A
B
, ,
Option B
C
, ,
Option C
D
, ,
Option D
6

What is the determinant of ?

Question illustration
A
–58
B
–7
C
4
D
58
7

A basketball player scored 33 points during a game by shooting 1-point free throws, 2-point field goals, and 3-point field goals. The player scored 17 times. She scored 3 more 2-point field goals than 1-point free throws. The system of equations below represents the situation, where x is the number of 1-point free throws, y is the number of 2-point field goals, and z is the number of 3-point field goals. x + y + z = 17x + 2y + 3z = 33y – x = 3Which matrix and solution represents the number of 1-point free throws, 2-point field goals, and 3-point field goals the player scored?

A
The player scored five 1-point free throws, eight 2-point field goals, and four 3-point field goals.
Option A
B
The player scored five 3-point field goals, eight 2-point field goals, and four 1-point free throws
Option B
C
The player scored seven 1-point free throws, four 2-point field goals, and six 3-point field goals.
Option C
D
The player scored seven 3-point field goals, four 2-point field goals, and six 1-point free throws.
Option D
8

What is the determinant of ?

Question illustration
A
–24
B
–3
C
3
D
45
9

What is the value of the element in row 1, column 1 of matrix X?

Question illustration
A
mc026-2.jpg
Option A
B
4
C
8y
D
0
10

Which would be the next step in solving for matrix A?

Question illustration
A
mc019-2.jpg
Option A
B
mc019-3.jpg
Option B
C
mc019-4.jpg
Option C
D
mc019-5.jpg
Option D
11

Given , , and .What is Y if ?

Question illustration
A
mc013-5.jpg
Option A
B
mc013-6.jpg
Option B
C
mc013-7.jpg
Option C
D
mc013-8.jpg
Option D
12

If A, B, and C represent three matrices of the same size and (A + B) + C = 0, then which statement is true?

A
and
Option A
B
mc016-3.jpg
Option B
C
mc016-4.jpg
Option C
D
mc016-5.jpg
Option D
13

A store sells almonds for $7 per pound, cashews for $10 per pound, and walnuts for $12 per pound. A customer buys 12 pounds of mixed nuts consisting of almonds, cashews, and walnuts for $118. The customer buys 2 more pounds of walnuts than cashews. The matrix below represents this situation.If the reduced row echelon form of this matrix represents the amount of each type of nut the customer buys, which statement is a possible interpretation of the results?

Question illustration
A
The customer buys 1 more pound of walnuts than almonds and 1 more pound of almonds than cashews.
B
The customer buys 2 more pounds of walnuts than almonds and 2 more pounds of almonds than cashews.
C
The customer buys 0.5 more pound of walnuts than almonds and 2.5 more pounds of almonds than cashews.
D
The customer buys 6.5 more pounds of walnuts than almonds and 8.5 more pounds of almonds than cashews.
14

Which matrix will always give a determinant of 0?

A
a matrix having all nonzero numbers
B
a matrix not being the identity matrix
C
a matrix not having equal rows
D
a matrix having two equal rows
15

What is the minimum value of C = 7x + 8y, given the constraints on x and y listed below?

Question illustration
3
32
4
42
4
46
6
64

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