Precalculus (6th Edition) Blitzer

Published by Pearson

Chapter 8 - Section 8.3 - Matrix Operations and Their Applications - Exercise Set - Page 918: 37

Answer

$4B-3C=\left[ \begin{matrix} 17 & 7 \\ -5 & -11 \\ \end{matrix} \right]$

Work Step by Step

Consider, \begin{align} & 4B-3C=4\left[ \begin{matrix} 5 & 1 \\ -2 & -2 \\ \end{matrix} \right]-3\left[ \begin{matrix} 1 & -1 \\ -1 & 1 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 4\times 5 & 4\times 1 \\ 4\times \left( -2 \right) & 4\times \left( -2 \right) \\ \end{matrix} \right]-\left[ \begin{matrix} 3\times 1 & 3\times \left( -1 \right) \\ 3\times \left( -1 \right) & 3\times 1 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 20 & 4 \\ -8 & -8 \\ \end{matrix} \right]-\left[ \begin{matrix} 3 & -3 \\ -3 & 3 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 20-3 & 4+3 \\ -8+3 & -8-3 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 17 & 7 \\ -5 & -11 \\ \end{matrix} \right] \end{align}

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