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: 32

Answer

a) $AB=\left[ \begin{matrix} 3 & 4 & -3 \\ -1 & 7 & -4 \\ 7 & 9 & -6 \\ \end{matrix} \right]$ b) $BA=\left[ \begin{matrix} 6 & -1 & -1 \\ -4 & -11 & 19 \\ 4 & -7 & 9 \\ \end{matrix} \right]$

Work Step by Step

(a) $\begin{align} & AB=\left[ \begin{matrix} 1 & -1 & 1 \\ 5 & 0 & -2 \\ 3 & -2 & 2 \\ \end{matrix} \right]\left[ \begin{matrix} 1 & 1 & 0 \\ 1 & -4 & 5 \\ 3 & -1 & 2 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 1\left( 1 \right)-1\left( 1 \right)+1\left( 3 \right) & 1\left( 1 \right)-1\left( -4 \right)+1\left( -1 \right) & 1\left( 0 \right)-1\left( 5 \right)+1\left( 2 \right) \\ 5\left( 1 \right)+0\left( 1 \right)-2\left( 3 \right) & 5\left( 1 \right)+0\left( -4 \right)-2\left( -1 \right) & 5\left( 0 \right)+0\left( -4 \right)-2\left( 2 \right) \\ 3\left( 1 \right)-2\left( 1 \right)+2\left( 3 \right) & 3\left( 1 \right)-2\left( -4 \right)+2\left( -1 \right) & 3\left( 0 \right)-2\left( 5 \right)+2\left( 2 \right) \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 1-1+3 & 1+4-1 & 0-5+2 \\ 5+0-6 & 5+0+2 & 0+0-4 \\ 3-2+6 & 3+8-2 & 0-10+4 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 3 & 4 & -3 \\ -1 & 7 & -4 \\ 7 & 9 & -6 \\ \end{matrix} \right] \end{align}$ (b) $\begin{align} & BA=\left[ \begin{matrix} 1 & 1 & 0 \\ 1 & -4 & 5 \\ 3 & -1 & 2 \\ \end{matrix} \right]\left[ \begin{matrix} 1 & -1 & 1 \\ 5 & 0 & -2 \\ 3 & -2 & 2 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 1\left( 1 \right)+1\left( 5 \right)+0\left( 3 \right) & 1\left( -1 \right)+1\left( 0 \right)+0\left( -2 \right) & 1\left( 1 \right)+1\left( -2 \right)+0\left( 2 \right) \\ 1\left( 1 \right)+\left( -4 \right)\left( 5 \right)+5\left( 3 \right) & 1\left( -1 \right)+\left( -4 \right)\left( 0 \right)+5\left( -2 \right) & 1\left( 1 \right)+\left( -4 \right)\left( -2 \right)+5\left( 2 \right) \\ 3\left( 1 \right)+\left( -1 \right)\left( 5 \right)+2\left( 3 \right) & 3\left( -1 \right)+\left( -1 \right)\left( 0 \right)+2\left( -2 \right) & 3\left( 1 \right)+\left( -1 \right)\left( -2 \right)+2\left( 2 \right) \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 1+5+0 & -1+0+0 & 1-2+0 \\ 1-20+15 & -1+0-10 & 1+8+10 \\ 3-5+6 & -3+0-4 & 3+2+4 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 6 & -1 & -1 \\ -4 & -11 & 19 \\ 4 & -7 & 9 \\ \end{matrix} \right] \end{align}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.