Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 11 - Systems of Equations and Inequalities - 11.4 Matrix Algebra - 11.4 Assess Your Understanding - Page 758: 21

Answer

$\begin{bmatrix} 25&-9\\ 4&20 \end{bmatrix}$

Work Step by Step

Refer to sum $\#15$ for determination of $AC$. $\implies I_{2} = \begin{bmatrix} 1&0\\ 0&1\end{bmatrix} \implies 3I_{2} = \begin{bmatrix}3&0\\0&3\end{bmatrix}$ $\implies \begin{bmatrix}28&-9\\4&23\end{bmatrix}-\begin{bmatrix}3&0\\0&3\end{bmatrix} = AC-3I_{2}$ We subtract matrices by subtracting the respective individual elements. $\therefore AC-3I_{2} = \begin{bmatrix} 28-3&-9-0\\ 4-0&23-3 \end{bmatrix} = \begin{bmatrix} 25&-9\\ 4&20 \end{bmatrix}$
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