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 - Concept and Vocabulary Check - Page 917: 7


The given statement is True.

Work Step by Step

Consider the matrix given below: $A=\left[ \begin{matrix} {{a}_{11}} & {{a}_{12}} \\ {{a}_{21}} & {{a}_{22}} \\ \end{matrix} \right]$ Then $\begin{align} & -4A=-4\left[ \begin{matrix} {{a}_{11}} & {{a}_{12}} \\ {{a}_{21}} & {{a}_{22}} \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} -4{{a}_{11}} & -4{{a}_{12}} \\ -4{{a}_{21}} & -4{{a}_{22}} \\ \end{matrix} \right] \end{align}$ We see that $-4A$ is obtained by multiplying each element of $A$ by $-4$. Therefore, the given statement is true.
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