AnswersAVA Algebra II w Statistics - S1Q1Matrices and Their Inverses

Matrices and Their Inverses — Unit test Answers

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A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?

A
The graph of the function is positive on (2, 4).
B
The graph of the function is negative on (4, ).
Option B
C
The graph of the function is positive on (, –7).
Option C
D
The graph of the function is negative on (–7, –1).
2
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Which property is shown in the matrix addition below?

Question illustration
A
associative property
B
identity property
C
inverse property
D
commutative property
3

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).
4

Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?

Question illustration
A
f(x) = x(x – a)2(x – b)4
B
f(x) = x(x – a)3(x – b)2
C
f(x) = x4(x – a)(x – b)2
D
f(x) = x2(x – a)5(x – b)
5

A polynomial function has a root of –6 with multiplicity 3 and a root of 2 with multiplicity 4. If the function has a negative leading coefficient and is of odd degree, which could be the graph of the function?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
6

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
7

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.
8

What is the end behavior of the graph of the polynomial function f(x) = –x5 + 9x4 – 18x3?

A
As , and as , .
Option A
B
As , and as , .
Option B
C
As , and as , .
Option C
D
As , and as , .
Option D
9

You can use a system of equations to graph and solve the polynomial equation . Which statement is true?

Question illustration
A
The system has one solution, and the equation has three zeroes.
B
The y-coordinates of the solutions to the system and the zeroes of the equation are not equal.
C
The x-coordinates of the solutions to the system and the zeroes of the equation are not equal.
D
The equation has one zero, and the system has three solutions.
10

What is the determinant of ?

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

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
12

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)
13

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

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
14

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

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
15

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

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