## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 10 - 10.2 - Operations with Matrices - 10.2 Exercises - Page 724: 14

#### Answer

Part A: $\begin{bmatrix} -1 & -1 & -2\\ -3 & 10 & 2\\ \end{bmatrix}$ Part B: $\begin{bmatrix} 3 & -1 & 8\\ 3 & 2 & 16\\ \end{bmatrix}$ Part C: $\begin{bmatrix} 3 & -3 & 9\\ 0 & 18 & 27\\ \end{bmatrix}$ Part D: $\begin{bmatrix} 7 & -3 & 19\\ 6 & 10 & 41\\ \end{bmatrix}$

#### Work Step by Step

Part A: $\begin{bmatrix} 1-2 & -1+0 & 3-5\\ 0-3 & 6+4 & 9-7\\ \end{bmatrix}$ = $\begin{bmatrix} -1 & -1 & -2\\ -3 & 10 & 2\\ \end{bmatrix}$ Part B: $\begin{bmatrix} 1+2 & -1-0 & 3+5\\ 0+3 & 6-4 & 9+7\\ \end{bmatrix}$ = $\begin{bmatrix} 3 & -1 & 8\\ 3 & 2 & 16\\ \end{bmatrix}$ Part C: $\begin{bmatrix} 3(1) & 3(-1) & 3(3)\\ 3(0) & 3(6) & 3(9)\\ \end{bmatrix}$ = $\begin{bmatrix} 3 & -3 & 9\\ 0 & 18 & 27\\ \end{bmatrix}$ Part D: First, find 2B: $\begin{bmatrix} 2(-2) & 2(0) & 2(-5)\\ 2(-3) & 2(4) & 2(-7)\\ \end{bmatrix}$ = $\begin{bmatrix} -4 & 0 & -10\\ -6 & 8 & -14\\ \end{bmatrix}$ Then, find 3A - 2B: $\begin{bmatrix} 3+4 & -3-0 & 9+10\\ 0+6 & 18-8 & 27+14\\ \end{bmatrix}$ = $\begin{bmatrix} 7 & -3 & 19\\ 6 & 10 & 41\\ \end{bmatrix}$

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