Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 8 - Section 8.3 - Matrix Operations and Their Applications - Exercise Set - Page 917: 23

Answer

$X=\left[ \begin{matrix} 7 & 27 \\ -8 & 36 \\ -17 & -4 \\ \end{matrix} \right]$

Work Step by Step

Consider the matrix equation, $B-X=4A$. This implies that, $X=B-4A$ or $X=B-4A$. Now we will consider, $\begin{align} & X=B-4A \\ & =\left[ \begin{matrix} -5 & -1 \\ 0 & 0 \\ 3 & -4 \\ \end{matrix} \right]-4\left[ \begin{matrix} -3 & -7 \\ 2 & -9 \\ 5 & 0 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} -5 & -1 \\ 0 & 0 \\ 3 & -4 \\ \end{matrix} \right]-\left[ \begin{matrix} -12 & -28 \\ 8 & -36 \\ 20 & 0 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 7 & 27 \\ -8 & 36 \\ -17 & -4 \\ \end{matrix} \right] \end{align}$
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