Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 10 - 10.2 - Operations with Matrices - 10.2 Exercises - Page 724: 21

Answer

$\begin{bmatrix} 10 & 8\\ -59 & 9\\ \end{bmatrix}$

Work Step by Step

We first add the two matrices within the parentheses to create matrix X: X = $\begin{bmatrix} 0-6 & -3+3\\ 7+8 & 2+1\\ \end{bmatrix}$ = $\begin{bmatrix} -6 & 0\\ 15 & 3\\ \end{bmatrix}$ We then multiply matrix X by -3 to create matrix A: A = $\begin{bmatrix} -6(-3) & 0(-3)\\ 15(-3) & 3(-3)\\ \end{bmatrix}$ = $\begin{bmatrix} 18 & 0\\ -45 & -9\\ \end{bmatrix}$ We then multiply the matrix not in the parentheses by 2 to create matrix B: B = $\begin{bmatrix} 4(2) & -4(2)\\ 7(2) & -9(2)\\ \end{bmatrix}$ = $\begin{bmatrix} 8 & -8\\ 14 & -18\\ \end{bmatrix}$ We then perform A - B: $\begin{bmatrix} 18-8 & 0+8\\ -45-14 & -9+18\\ \end{bmatrix}$ = $\begin{bmatrix} 10 & 8\\ -59 & 9\\ \end{bmatrix}$
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