## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 10 - 10.2 - Operations with Matrices - 10.2 Exercises - Page 725: 53

#### Answer

$\begin{bmatrix} 5 & 8\\ -4 & -16\\ \end{bmatrix}$

#### Work Step by Step

First multiply the two leftmost matrices: $\begin{bmatrix} 3 & 1\\ 0 & -2\\ \end{bmatrix}$$\begin{bmatrix} 1 & 0\\ -2 & 2\\ \end{bmatrix} = \begin{bmatrix} 3(1) + 1(-2) & 3(0) + 1(2)\\ 0(1) + (-2)(-2) & 0(0) + (-2)(2)\\ \end{bmatrix} = \begin{bmatrix} 3-2 & 0+2\\ 0+4 & 0-4\\ \end{bmatrix} = \begin{bmatrix} 1 & 2\\ 4 & -4\\ \end{bmatrix} We then take the matrix from above and multiply it with the rightmost matrix: \begin{bmatrix} 1 & 2\\ 4 & -4\\ \end{bmatrix}$$\begin{bmatrix} 1 & 0\\ 2 & 4\\ \end{bmatrix}$ = $\begin{bmatrix} 1(1) + 2(2) & 1(0) + 2(4)\\ 1(4) + 2(-4) & 4(0) + (-4)(4)\\ \end{bmatrix}$ = $\begin{bmatrix} 1+4 & 0+8\\ 4-8 & 0-16\\ \end{bmatrix}$ = $\begin{bmatrix} 5 & 8\\ -4 & -16\\ \end{bmatrix}$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.