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: Which of the following scenarios would result in an undefined matrix addition?

Adding a $$2 \times 3$$ matrix to a $$3 \times 2$$ matrix

Q: A factory produces a product that requires 3 hours in assembly at $$9/hour$$ and 1 hour in finishing at $$6/hour. $$Using matrix multiplication, what is the total labor cost per product?

$$3 \times 9 + 1 \times 6 = 33$$

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: A salesperson receives a 5% commission on gross sales. If their September sales for two models are represented by the matrix $$\begin{bmatrix} 20000 & 15000 \\ 18000 & 22000 \end{bmatrix}$$, what is the commission matrix?

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

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

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 6

A company pays its assembly workers $$12 per hour and finishing workers 7 $$per hour in California. If a trick ski requires 5 hours of assembly and 1.5 hours of finishing, what is the total labor cost for producing one trick ski in California?

Accepted Answer

$$60 + 10.5 = 70.5$$

Question 7

Which of the following is a zero matrix?

Accepted Answer

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

Question 8

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 9

Which of the following scenarios would result in an undefined matrix addition?

Accepted Answer

Adding a $$2 	imes 3$$ matrix to a $$3 	imes 2$$ matrix

Question 10

A factory produces a product that requires 3 hours in assembly at $$9/hour$$ and 1 hour in finishing at $$6/hour. $$Using matrix multiplication, what is the total labor cost per product?

Accepted Answer

$$3 	imes 9 + 1 	imes 6 = 33$$

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

Which of the following best describes the result of multiplying a $$2 	imes 3$$ matrix by a $$3 	imes 1$$ matrix?

Accepted Answer

A $$2 	imes 1$$ matrix

Question 13

If $$A is a$$ $$2 	imes 3$$ matrix and $$B is a$$ $$3 	imes 2$$ matrix, which of the following statements is TRUE?

Accepted Answer

Both $$AB$$ and $$BA$$ are defined.

Question 14

A salesperson receives a 5% commission on gross sales. If their September sales for two models are represented by the matrix $$\begin{bmatrix} 20000 & 15000 \ 18000 & 22000 \end{bmatrix}$$, what is the commission matrix?

Accepted Answer

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

Question 15

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

Accepted Answer

Distributive property over matrix multiplication

Study Guide: Matrices and Basic Operations in College Algebra

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