Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 2 - Section 2.6 - Matrices - Exercises - Page 184: 4

Answer

a) $AB=\begin{matrix}-1&1&0 \\0&1&-1 \\1&-2&1\end{matrix}$ b) $AB=\begin{matrix}4&-1&-7&6 \\-7&-5&8&5 \\4&0&7&3\end{matrix}$ c) $AB=\begin{matrix}2&0&-3&-4&-1 \\24&-7&20&29&2 \\-10&4&-17&-24&-3\end{matrix}$

Work Step by Step

a)$\begin{matrix} 0+0-1&1+0+0&-1+0+1 \\0-1+1&0+1+0&0+0-1 \\0+1+0&-1-1+0&1+0+0\end{matrix}=\begin{matrix}-1&1&0 \\0&1&-1 \\1&-2&1\end{matrix}$ b)$\begin{matrix} 1+3+0&-1+0+0&2-9+0&3+3+0 \\1-2-6&-1+0-4&2+6+0&3-2+4 \\2-1+3&-2+0+2&4+3+0&6-1-2\end{matrix}=\begin{matrix}4&-1&-7&6 \\-7&-5&8&5 \\4&0&7&3\end{matrix}$ c)$\begin{matrix}0+2&0+0&0-3&0-4&0-1 \\ 28-4&-7+0&14+6&21+8&0+2 \\-16+6&4+0&-8-9&0-3\end{matrix}=\begin{matrix}2&0&-3&-4&-1 \\24&-7&20&29&2 \\-10&4&-17&-24&-3\end{matrix}$
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