Quiz about Unit 10 Individual Practice

Question 1

For which matrix A is the following matrix equation always true? [A][M]=[M]

Accepted Answer

$$\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 0 & 1 \ 1 & 0 \end{bmatrix}$$

Question 2

Given that a 2 x 2 matrix M satisfies the equation [A][M] = [M] for all possible 2 x 2 matrices A, which matrix M satisfies this equation?

Accepted Answer

$$\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 0 & 1 \ 1 & 0 \end{bmatrix}$$

Question 3

If $$\begin{bmatrix} -3 & 1 \ 2 & -7 \end{bmatrix}$$ *[B]= $$\begin{bmatrix} -3 & 1 \ 2 & -7 \end{bmatrix}$$ , then [B] equals:

Accepted Answer

Answer

$$\begin{bmatrix} -3 & 1 \ 2 & -7 \end{bmatrix}$$

Question 4

Consider the matrix being multiplied by t. What is the value of t?

Accepted Answer

1/2

Answer

2

Answer

-1/2

Answer

-2

Question 5

What is the value of t?

Accepted Answer

-2

Answer

2

Answer

1

Answer

3

Question 6

What is the value of t?

Accepted Answer

-3

Answer

2

Answer

1

Answer

-2

Question 7

The chart shows the number of students in fall sports and spring sports by grade and gender. Which of the following could be used to find the total number of girls and boys in all sports by grade levels?

Accepted Answer

Question 8

Which of the following could be used to find the total number of girls and boys in band and choir by grade levels?

Accepted Answer

Question 9

Select the matrices that would be added to represent the total number of girls and boys in math and science clubs by grade levels.

Accepted Answer

Accepted Answer

Question 10

Select the matrices that would be used in an addition expression that could be used to find the total number of girls and boys in football and soccer clubs by grade levels?

Accepted Answer

Accepted Answer

Question 11

Which of the following could be used to find the total number of girls and boys in drama and debate clubs by grade levels?

Accepted Answer

Question 12

What is the product of

Accepted Answer

Question 13

What is the product of

Accepted Answer

Question 14

What is the product of

Accepted Answer

Question 15

20. What is the product of $$\begin{bmatrix} 3 & 8 \ 4 & 6 \end{bmatrix} \begin{bmatrix} 7 & 2 \ 5 & 0 \end{bmatrix}$$ ? Choose the correct result in the form of a matrix.

Accepted Answer

$$\begin{bmatrix} 61 & 6 \ 58 & 8 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 61 & 8 \ 58 & 6 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 28 & 40 \ 4 & 6 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 21 & 6 \ 30 & 8 \end{bmatrix}$$

Question 16

Matrix R has dimensions of 3 x 1. Which matrices can be added to matrix R?

Accepted Answer

$$\begin{bmatrix} 4 \ -2 \ 0 \end{bmatrix}$$

Accepted Answer

$$\begin{bmatrix} -2 \ -4 \ 7 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 1 & 6 & 5 \ -8 & 9 & -1 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 10 & 13 \ 6 & -8 \ 5 & 18 \end{bmatrix}$$

Question 17

Matrix A has dimensions of 2 x 3. Which matrix can be added to matrix A?

Accepted Answer

$$\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 7 & 8 \ 9 & 10 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 3 \ -2 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 2 & 4 \ 6 & 3 \ 5 & 7 \end{bmatrix}$$

Question 18

25. Matrix C has dimensions of 3 x 1. Which matrices can be added to matrix C?

Accepted Answer

b. $$\begin{bmatrix} 10 \ 12 \ 14 \end{bmatrix}$$

Accepted Answer

d. $$\begin{bmatrix} 4 \ 2 \ 5 \end{bmatrix}$$

Answer

a. $$\begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}$$

Answer

c. $$\begin{bmatrix} 3 & 4 \ 5 & 6 \ 7 & 8 \end{bmatrix}$$

Question 19

The matrices show the results of the recreational softball season.

How many games did team B play over the two-year period?

Accepted Answer

21

Answer

12

Answer

17

Answer

8

Question 20

How many games did the team C play over the two-year period?

Accepted Answer

27

Answer

24

Answer

18

Answer

32

Question 21

The matrices show the number of tournaments won and lost by different chess clubs. How many total tournaments Club Y play over the two-year period?

Accepted Answer

15

Answer

20

Answer

18

Answer

22

Question 22

Question 22.

Accepted Answer

[-29 -4]

Answer

[29 4]

Answer

[-29 4 0]

Answer

[29 4 0]

Question 23

Calculate the product:

Accepted Answer

[30 1]

Answer

[-30 1]

Answer

[30 -1]

Answer

[-30 -1]

Question 24

Find the result of the matrix multiplication:

Accepted Answer

[18 -9]

Answer

[-18 9]

Answer

[18 9 0]

Answer

[-18 -9]

Question 25

Matrix A represents the number of tickets sold for three different movies at two separate theaters in March. Matrix B represents the number of tickets sold for the same movies at the same locations in April.

Write a matrix that shows how many more tickets were sold in April for Theater 1.

Accepted Answer

[10 10 10]

Answer

[10 5 10]

Answer

[5 10 5]

Answer

[15 5 10]

Question 26

Matrix P represents the number of different types of laptops sold at two different stores in May. Matrix Q represents the number of laptops sold at the same stores in June.

Write a matrix that shows how many more laptops were sold in June for Store 1.

Accepted Answer

[5 5 5]

Answer

[5 4 6]

Answer

[4 5 4]

Answer

[6 5 4]

Question 27

Matrix M represents the number of meals sold at two different restaurants on weekdays in January (chicken, beef and pork). Matrix N represents the number of meals sold at the same restaurant in February.

Write a matrix that shows how many more meals were sold in February for restaurant 2.

Accepted Answer

[5 10 10]

Answer

[10 5 10]

Answer

[10 10 5]

Answer

[5 10 5]

Question 28

If A = $$\begin{bmatrix} -3 & 11 & 4 \ 0 & -2 & 7 \end{bmatrix}$$ , then the value of 5A is

Accepted Answer

$$\begin{bmatrix} -15 & 55 & 20 \ 0 & -10 & 35 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 15 & -55 & -20 \ 0 & 10 & -35 \end{bmatrix}$$

Answer

$$\begin{bmatrix} -15 & 11 & 20 \ 0 & -10 & 35 \end{bmatrix}$$

Answer

$$\begin{bmatrix} -3 & 11 & 4 \ 0 & -2 & 7 \end{bmatrix}$$

Question 29

42. If B = $$\begin{bmatrix} 2 & -5 & 8 \ 3 & 0 & -7 \end{bmatrix}$$ , what is the value of 4B?

Accepted Answer

$$\begin{bmatrix} 8 & -20 & 32 \ 12 & 0 & -28 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 6 & -10 & 16 \ 9 & 0 & -14 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 8 & -20 & 32 \ 12 & 0 & -30 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 8 & -15 & 32 \ 12 & 0 & -28 \end{bmatrix}$$

Question 30

43. If C = $$\begin{bmatrix} -6 & 3 & 9 \ 4 & -1 & 5 \ 2 & -2 & 5 \end{bmatrix}$$ , find the value of -2C. Choose the correct value of -2C.

Accepted Answer

$$\begin{bmatrix} 12 & -6 & -18 \ -8 & 2 & -10 \ -4 & 4 & -10 \end{bmatrix}$$

Answer

$$\begin{bmatrix} -12 & 6 & 18 \ 8 & -2 & 10 \ 4 & -4 & 10 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 12 & -6 & -18 \ -8 & 2 & -10 \ -4 & 4 & -11 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 12 & 6 & 18 \ -8 & -2 & -10 \ -4 & -4 & -10 \end{bmatrix}$$

Question 31

A matrix A is given as: A = $$\begin{bmatrix} -3 & 11 & 4 \ 0 & -2 & 7 \end{bmatrix}$$ A scalar multiplication operation is performed on A using the scalar 5, resulting in matrix B: B=5A Which of the following correctly represents matrix B?

Accepted Answer

Question 32

A matrix A is given as: $$A = \begin{bmatrix} -3 & 11 & 4 \ 0 & -2 & 7 \end{bmatrix}$$ After multiplying A by a scalar k, the resulting matrix B is: $$B = \begin{bmatrix} -12 & 44 & 16 \ 0 & -8 & 28 \end{bmatrix}$$ What is the value of k?

Accepted Answer

C. 4

Answer

A. 2

Answer

B. 3

Answer

D. 5

Question 33

Consider the matrices: If C = A - B, what is matrix C?

Accepted Answer

Question 34

Given the matrices: $$X = \begin{bmatrix} 4 & 7 \ -3 & 5 \end{bmatrix}$$ $$Y = \begin{bmatrix} 1 & -2 \ 6 & 3 \end{bmatrix}$$ find the matrix $$Z = X - Y$$ . Choose the correct resultant matrix.

Accepted Answer

$$Z = \begin{bmatrix} 3 & 9 \ -9 & 2 \end{bmatrix}$$

Answer

$$Z = \begin{bmatrix} 5 & 5 \ -9 & 8 \end{bmatrix}$$

Answer

$$Z = \begin{bmatrix} 3 & 2 \ -9 & 2 \end{bmatrix}$$

Answer

$$Z = \begin{bmatrix} 4 & 7 \ -3 & 5 \end{bmatrix}$$

Question 35

Calculate $$M - N$$ where $$M = \begin{bmatrix} -2 & 8 \ 5 & -1 \end{bmatrix}$$ and $$N = \begin{bmatrix} 4 & -3 \ -7 & 6 \end{bmatrix}$$ and write your answer as a matrix.

Accepted Answer

$$\begin{bmatrix} -6 & 11 \ 12 & -7 \end{bmatrix}$$

Answer

$$\begin{bmatrix} 6 & -11 \ -12 & 7 \end{bmatrix}$$

Answer

$$\begin{bmatrix} -2 & 8 \ 5 & -1 \end{bmatrix}$$

Answer

$$\begin{bmatrix} -6 & 11 \ -12 & 7 \end{bmatrix}$$

Question 36

Consider the matrices: If R = P - Q which of the following represents matrix R?

Accepted Answer

Question 37

A and B are 3 x 3 matrices.

Write a matrix to represent the sum of A and B.

Accepted Answer

Question 38

Matrices A and B are given as:

Which matrix represents the sum of A and B?

Accepted Answer

Question 39

Matrices X and Y are given as:

Which matrix represents the sum of X and Y?

Accepted Answer

Question 40

If:

Find the sum M and N. Choose the correct result.

Accepted Answer

Question 41

55. Consider the column matrices:

What is the sum A + B?

Accepted Answer

Question 42

When Matrix K is added to Matrix M, the result is Matrix K. Which of the following matrices could be Matrix M?

Accepted Answer

Question 43

Matrix L is given by:

When Matrix L is added to Matrix M, the result is Matrix L. Which of the following could be Matrix L

Accepted Answer

Question 44

Matrix A is given by:

When Matrix A is added to Matrix N, the result is Matrix A, which of the following could be Matrix N?

Accepted Answer

Question 45

Matrix B is given by:

When Matrix B is added to Matrix P, the result is Matrix B. Which could be Matrix P?

Accepted Answer

Question 46

Matrix C is given by: $$[C]=\begin{bmatrix} -1 & 9 & 2 \ 8 & -3 & 7 \ 4 & 6 & -5 \end{bmatrix}$$ When Matrix C is added to Matrix Q, the result is Matrix C. Write Matrix Q as a multiple choice answer.

Accepted Answer

Matrix Q = zero matrix

Answer

Matrix Q = identity matrix

Answer

Matrix Q = Matrix C

Answer

Matrix Q = matrix with all entries equal to one

Question 47

$$\begin{bmatrix} 9 \ 2 \ 5 \end{bmatrix} imes [1 \ 7 \ 4] = i$$

Accepted Answer

$$\begin{bmatrix} 9 & 63 & 36 \ 2 & 14 & 8 \ 5 & 35 & 20 \end{bmatrix}$$

Answer

Answer

$$[9 \ 14 \ 20]$$

Answer

$$\begin{bmatrix} 9 & 2 & 5 \ 63 & 14 & 35 \ 36 & 8 & 20 \end{bmatrix}$$

Question 48

What is A x B?

Accepted Answer

Question 49

Find X x Y.

Accepted Answer

Question 50

Find P x Q.

Accepted Answer

Question 51

Given the matrices:

Find the product A x B and write the resulting matrix.

Accepted Answer

Question 52

Given the matrices:

Find the product X x Y and write the resulting matrix.

Accepted Answer

Question 53

Martix L is shown.

When Matrix L is multiplied by Matrix K, the result is Matrix L, as shown by the equation LK = L. Which of the following is Matrix K?

Accepted Answer

Question 54

Matrix M is shown below:

When Matrix M is multiplied by Matrix N, the result is Matrix M, as shown by the equation MN = M. Which of the following is matrix N?

Accepted Answer

Question 55

Matrix P is given as:

If PQ = P, which of the following could be Matrix Q?

Accepted Answer

Question 56

Matrix R is shown:

If RS = R, which of the following is matrix S?

Accepted Answer

Question 57

71. Matrix X is given as:

If XY = X, determine Matrix Y.

Accepted Answer

Question 58

Matrix T is given as:

If XY = X, determine Matrix Y.

Accepted Answer

Question 59

The matrix below represents a football team's performance over 3 games. Each row represents a different game. The number of points scored by the football team are in the first column and the number of points they allowed are in the second column. Which of the following statements are true? Select the three that apply.

Accepted Answer

b. In the third game, the team scored 22 points.

Accepted Answer

c. The team won the third game.

Accepted Answer

d. Two times the team allowed more than 15 points.

Answer

a. In the second game, the team allowed 30 points.

Answer

e. The least number of points the team allowed was 12.

Question 60

The matrix below represents a basketball team's performance over 3 games. Each row represents a different game. The number of points scored by the basketball team is in the first column, and the number of points allowed is in the second column.

Which of the following statements are true? Select the three that apply.

Accepted Answer

The team scored 72 points in the second game.

Accepted Answer

The team won the first game.

Accepted Answer

The team allowed more than 50 points in two games.

Answer

The least number of points the team allowed was 65.

Answer

The team won the third game.

Question 61

The matrix below represents a soccer team's performance over four games. Each row represents a different game. The first column shows goals scored by the team, and the second column shows goals allowed. Which of the following statements are true? Select the FOUR that apply.

Accepted Answer

The team won the first game.

Accepted Answer

The team won the fourth game.

Accepted Answer

The team allowed more than 2 goals in two games.

Accepted Answer

The least number of goals the team allowed was 1.

Answer

In the second game, the team allowed 2 goals.

Question 62

A bakery sells loaves of bread in three sizes and two flavors. The baker has baked 14 small pumpernickel loaves, 10 medium pumpernickel loaves, and 8 large pumpernickel loaves. He also baked 18 small sourdough loaves, 15 medium sourdough loaves, and 12 large sourdough loaves. Which matrix could be used to represent this data if rows represent the type of bread, and the columns represent the size of the loaf of bread?

Accepted Answer

Question 63

A fruit vendor sells apples and oranges in three different sizes: small, medium, and large. The vendor has stocked 25 small apples, 18 medium apples, and 12 large apples. He also stocked 20 small oranges, 15 medium oranges, and 10 large oranges. Which matrix could be used to represent this data if columns represent the type of fruit and the rows represent the size?

Accepted Answer

Question 64

A coffee shop sells coffee in three sizes: small, medium, and large. They track the number of cups sold in two different flavors: regular and decaf. The shop sold 40 small regular coffees, 30 medium regular coffees, and 25 large regular coffees. They also sold 35 small decaf coffees, 20 medium decaf coffees, and 15 large decaf coffees.

Which matrix correctly represents this data if rows represent the type of coffee and columns represent the cup sizes?

Accepted Answer

Unit 10 Individual Practice

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