Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 2 - Matrix Algebra - 2.1 Exercises - Page 102: 4

Answer

$A-5I_{3}=\begin{bmatrix}4&-1&3\\-8&2&-6\\-4&1&3\end{bmatrix}$ $(5I_{3})A=\begin{bmatrix}45&-5&15\\ -40&35&-30\\ -20&5&40 \end{bmatrix}$

Work Step by Step

$5I_{3}=\begin{bmatrix}5&0&0\\0&5&0\\0&0&5\end{bmatrix}$ $ \begin{align} A-5I_{3}&=\begin{bmatrix}9-5&-1-0&3-0\\-8-0&7-5&-6-0\\-4-0&1-0&8-5\end{bmatrix}\\ &=\begin{bmatrix}4&-1&3\\-8&2&-6\\-4&1&3\end{bmatrix} \end{align} $ $ \begin{align} (5I_{3})A &=\begin{bmatrix}(5I_{3})\begin{bmatrix}9\\-8\\-4\end{bmatrix}&(5I_{3})\begin{bmatrix}-1\\7\\1\end{bmatrix}&(5I_{3})\begin{bmatrix}3\\-6\\8\end{bmatrix}\end{bmatrix}\\ &=\begin{bmatrix}45&-5&15\\ -40&35&-30\\ -20&5&40 \end{bmatrix} \end{align} $
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