Q: Given matrices $$A = \begin{bmatrix} 2 & -3 & 0 \\ 1 & 2 & -5 \end{bmatrix}$$ and $$B = \begin{bmatrix} 3 & 2 & 7 \\ -2 & 3 & -2 \end{bmatrix}$$, what is $$A + B$$?

$$\begin{bmatrix} 5 & -1 & 7 \\ -1 & 5 & -7 \end{bmatrix}$$

Q: If $$M = \begin{bmatrix} 4 & -2 \\ 0 & 7 \end{bmatrix}$$, what is $$-M$$?

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

Q: Which of the following is a zero matrix?

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

Q: If $$A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}$$, what is $$2A - B$$?

$$\begin{bmatrix} -3 & -2 \\ -1 & 0 \end{bmatrix}$$

Q: A car dealership pays 5% commission on gross sales. If September sales for two models by two salespeople are represented by $$S = \begin{bmatrix} 20000 & 15000 \\ 18000 & 22000 \end{bmatrix}$$, what is the commission matrix?

$$\begin{bmatrix} 1000 & 750 \\ 900 & 1100 \end{bmatrix}$$

Q: If $$A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$$, what is $$AB$$?

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

Q: If $$A = \begin{bmatrix} 2 & 1 \\ 0 & 3 \end{bmatrix}$$ and $$B = \begin{bmatrix} 1 & 0 \\ 4 & 5 \end{bmatrix}$$, what is $$A - B$$?

$$\begin{bmatrix} 1 & 1 \\ -4 & -2 \end{bmatrix}$$

Question 1

Which of the following statements about matrix addition is TRUE?

Accepted Answer

Matrix addition is only defined for matrices of the same size.

Question 2

Given matrices $$A = \begin{bmatrix} 2 & -3 & 0 \ 1 & 2 & -5 \end{bmatrix}$$ and $$B = \begin{bmatrix} 3 & 2 & 7 \ -2 & 3 & -2 \end{bmatrix}$$, what is $$A + B$$?

Accepted Answer

$$\begin{bmatrix} 5 & -1 & 7 \ -1 & 5 & -7 \end{bmatrix}$$

Question 3

If $$M = \begin{bmatrix} 4 & -2 \ 0 & 7 \end{bmatrix}$$, what is $$-M$$?

Accepted Answer

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

Question 4

Which property is illustrated by the equation $$A + B = B + A$$ for matrices $$A$$ and $$B of $$the same size?

Accepted Answer

Commutative property

Question 5

A company pays its workers $$15 per hour for assembly and 10 $$per hour for finishing. If a product requires 2 hours of assembly and 3 hours of finishing, what is the total labor cost per product using matrix multiplication?

Accepted Answer

$$\60$

Question 6

Which of the following is a zero matrix?

Accepted Answer

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

Question 7

If $$A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix}$$, what is $$2A - B$$?

Accepted Answer

$$\begin{bmatrix} -3 & -2 \ -1 & 0 \end{bmatrix}$$

Question 8

Which of the following must be true for the product $$AB of $$matrices $$A$$ and $$B to be $$defined?

Accepted Answer

The number of columns in $$A$$ equals the number of rows in $$B.$$

Question 9

Suppose $$A is a$$ $$2 	imes 3$$ matrix and $$B is a$$ $$3 	imes 4$$ matrix. What is the size of the product $$AB$$?

Accepted Answer

$$2 	imes 4$$

Question 10

A car dealership pays 5% commission on gross sales. If September sales for two models by two salespeople are represented by $$S = \begin{bmatrix} 20000 & 15000 \ 18000 & 22000 \end{bmatrix}$$, what is the commission matrix?

Accepted Answer

$$\begin{bmatrix} 1000 & 750 \ 900 & 1100 \end{bmatrix}$$

Question 11

If $$A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$$ and $$B = \begin{bmatrix} 0 & 1 \ 1 & 0 \end{bmatrix}$$, what is $$AB$$?

Accepted Answer

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

Question 12

A factory produces two types of skis. The labor-hours per ski are $$L = \begin{bmatrix} 5 & 3 \ 1.5 & 1 \end{bmatrix}$$ and the hourly wages at two plants are $$H = \begin{bmatrix} 12 & 7 \ 13 & 8 \end{bmatrix}. $$What does the product $$LH$$ represent?

Accepted Answer

The total labor cost for each ski at each plant.

Question 13

If $$A = \begin{bmatrix} 2 & 1 \ 0 & 3 \end{bmatrix}$$ and $$B = \begin{bmatrix} 1 & 0 \ 4 & 5 \end{bmatrix}$$, what is $$A - B$$?

Accepted Answer

$$\begin{bmatrix} 1 & 1 \ -4 & -2 \end{bmatrix}$$

Question 14

Which of the following is NOT a property of matrix addition?

Accepted Answer

Distributive property over multiplication

Question 15

If $$k = 3$$ and $$M = \begin{bmatrix} 2 & -1 \ 0 & 4 \end{bmatrix}$$, what is $$kM$$?

Accepted Answer

$$\begin{bmatrix} 6 & -3 \ 0 & 12 \end{bmatrix}$$

Question 16

Given $$A = \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \end{bmatrix}$$ and $$B = \begin{bmatrix} 7 & 8 \ 9 & 10 \ 11 & 12 \end{bmatrix}$$, what is the $$(1,2)$$ entry of $$AB$$?

Accepted Answer

$$1 	imes 8 + 2 	imes 10 + 3 	imes 12 = 8 + 20 + 36 = 64$$

Study Guide: Matrices and Basic Operations in College Algebra

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