AnswersPrecalculusDeterminants

Determinants — Unit test Answers

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1
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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
2
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Matrix P is shown below. Given that Matrix P equals Matrix Q, what is the value of

Question illustration
A
3.5
B
6.2
C
7
D
16
3

A triangle is located on a three-dimensional coordinate plane. Matrix A shows the location of each vertex, where the first column represents the x coordinate, the second column represents the y coordinate, and the third column represents the z coordinate.The triangle is dilated by a scale factor of 2, then translated by the factors in matrix B, resulting in an image triangle as represented by the equation below.In which directions are the vertices translated, as indicated by matrix B?

Question illustration
A
3 units in the x direction, -2 units in the y direction, 1 unit in the z direction
B
3 units in the x direction, 3 units in the y direction, 3 unit in the z direction
C
4 units in the x direction, 0 units in the y direction, 2 unit in the z direction
D
4 units in the x direction, 6 units in the y direction, 5 unit in the z direction
4

The linear system below represents the sales of large and small popcorn servings at a movie theater for two consecutive days.What is the size of the augmented matrix for this system?

Question illustration
A
mc007-2.jpg
Option A
B
mc007-3.jpg
Option B
C
mc007-4.jpg
Option C
D
mc007-5.jpg
Option D
5

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
6

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
7

What is the area of a triangle with vertices at (–3, 3), (2, 3), and (4, 7)?

A
5 square units
B
10 square units
C
20 square units
D
40 square units
8

Ines created a coefficient matrix to represent the system of linear equations below.Which type of matrix did Ines create?

Question illustration
A
a matrix
Option A
B
a matrix
Option B
C
an augmented matrix
D
a diagonal matrix
9

Matrix X is shown below.If matrices X and Y are equal, what is the value of

Question illustration
A
7.5
B
27
C
40
D
49.5
10

What is the determinant of ?

Question illustration
A
–58
B
–7
C
4
D
58
11

Which matrix equation can be used to solve the systems of equations below?3x - 2y = -36x - 5y = -9

A
mc016-1.jpg
Option A
B
mc016-2.jpg
Option B
C
mc016-3.jpg
Option C
D
mc016-4.jpg
Option D
12

What is the determinant of ?

Question illustration
A
–24
B
–3
C
3
D
45
13

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
14

Calvin encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, he multiplied the clear text code for each letter by the matrix to get a matrix that represents the encoded text. The matrix representing the encoded text is . What is the secret phrase? Determine the location of spaces after you decode the text.

Question illustration
A
MY COLOR IS GREEN
B
BLUE IS THE COLOR
C
GREEN IS MY COLOR
D
THE COLOR IS BLUE
15

The vertices of a rectangle are given in the columns of the matrix . If is found to perform a transformation, what are the coordinates of the transformed rectangle?

Question illustration
A
(0, 0), (0, 18), (18, 18), (18, 0)
B
(0, 0), (18, 0), (18, –18), (0, –18)
C
(0, 0), (–18, 0), (–18, –18), (0, –18)
D
(0, 0), (18, 0), (18, 18), (0, 18)
16

What is the product?

Question illustration
A
mc018-2.jpg
Option A
B
mc018-3.jpg
Option B
C
mc018-4.jpg
Option C
D
mc018-5.jpg
Option D
17

The vertices of a triangle are given in the columns of the matrix . If is found to perform a transformation, what are the coordinates of the transformed triangle?

Question illustration
A
(0, 0), (–4, 0), (0, –5)
B
(0, 0), (–4, 0), (0, 5)
C
(0, 0), (4, 0), (0, –5).
D
(0, 0), (4, 0), (0, 5).
18

Which property is shown in the matrix addition below?

Question illustration
A
associative property
B
identity property
C
inverse property
D
commutative property
19

Matrices X and Y both measure and are inverses of each other. Which matrix represents their product?

Question illustration
A
mc007-2.jpg
Option A
B
mc007-3.jpg
Option B
C
mc007-4.jpg
Option C
D
mc007-5.jpg
Option D
20

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.

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