AnswersAVA Algebra II w Statistics - S1Q1Matrices and Their Inverses

Matrices and Their Inverses — Unit test Answers

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What is the product?

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Option
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Option B
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Option C
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Option D
2
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Suppose matrix D is the inverse of matrix C. Which of the following is equal to D?

A
CDD
B
CCD
C
DDD
D
CCC
3

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

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A
f(x) = x2(x – a)2(x – b)4(x – c)
B
f(x) = x3(x – a)3(x – b)(x – c)2
C
f(x) = x4(x – a)(x – b)3(x – c)3
D
f(x) = (x – a)2(x – b)(x – c)6
4

The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect?

A
She is incorrect because systems may have only complex solutions which are not visible on a graph.
B
She is incorrect because the solutions may have multiplicity greater than 1.
C
She is correct because all solutions are intersection points of the graphs.
D
She is correct because the solutions are irrational.
5

What is the value of C in the matrix equation below?

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6

What is the product?

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Option A
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Option C
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Option D
7

Jonas made the following matrix of temperatures for the first 4 days of January. He also made the following matrix of temperatures for the first 4 days of February. Which matrix shows the difference of January and February?

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8

A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.

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A
4 inches
B
5 inches
C
9 inches
D
10 inches
9

Raj 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.

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A
YUMMY IS THE CORN
B
THE TOMATO IS RED
C
THE CORN IS YUMMY
D
RED IS THE TOMATO
10

Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?

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Option A
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Option D
11

Which of the following sets of data would you likely represent with a square matrix?

A
A shoe salesperson wants to use an augmented matrix to represent the quantity of children’s shoes and adult shoes sold at his store for two days.
B
A racquetball club has a tournament where each member plays every other member and represents the scores in a matrix.
C
A student wants to write a coefficient matrix representing a linear system with two equations and three unknowns.
D
A teacher wants to write an augmented matrix representing a linear system with four equations and four unknowns.
12

Jelani wrote the system of linear equations below to represent the number of student and adult tickets he and his friend sold to their school play.Jelani also wrote the augmented matrix to represent this system. Which matrix could Jelani have written?

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13

What is the determinant of the coefficient matrix of the system ?

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A
–158
B
–117
C
65
D
117
14

If and , then which statement is true?

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A
det(A) = det(B)
B
det(A) = –det(B)
C
det(A) ¹ 0 and det(B) = 0
D
det(A) = 0 and det(B) ¹ 0
15

A polynomial function has a root of –6 with multiplicity 1, a root of –2 with multiplicity 3, a root of 0 with multiplicity 2, and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about the graph is true?

A
The graph of the function is positive on (–6, –2).
B
The graph of the function is negative on (, 0).
Option B
C
The graph of the function is positive on (–2, 4).
D
The graph of the function is negative on (4, ).
Option D
16

Each column of the matrix represents a vertex of a rectangle on the coordinate plane. If Fan scales the rectangle by finding 4A, what are the vertices of the scaled rectangle?

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A
(4, 4), (24, 4), (24, 20), (4, 20)
B
(5, 5), (10, 5), (10, 9), (5, 9)
C
(4, 4), (6, 1), (6, 5), (1, 5)
D
(5, 5), (6, 1), (6, 5), (4, 20)
17

Which value of x makes the two matrices inverses of each other?

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A
–2
B
–1
C
1
D
2
18

The matrix represents the length of 12 in. and the width of 4 in. of a rectangle. If matrix multiplication is used to double the length and width of the rectangle, which rectangle represents the result of the matrix multiplication?

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19

A polynomial function has a root of –3 with multiplicity 2, a root of 0 with multiplicity 1, a root of 1 with multiplicity 1, and a root of 3 with multiplicity 2. If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?

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Option A
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Option D
20

What is the value of given the matrix equation below?

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A
2
B
8
C
26
D
28

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