College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 8 - Section 8.4 - Matrix Algebra - 8.4 Assess Your Understanding - Page 598: 26


$\left[\begin{array}{cccc} {-22}&{29}&{8}&{-1}\\ {-10}&{17}&{6}&{-1}\end{array}\right]$

Work Step by Step

Let $A$ denote an $m$ by $\fbox{$r$}$ matrix and let $B$ denote an $\fbox{$r$}$ by $n$ matrix. The product $AB$ is defined as the $m$ by $n$ matrix whose entry in row $i,$ column $j$ is the product of the $i$ th row of $A$ and the $j$ th column of $B$ . --- $A$ is a $2$ by $\fbox{$2$}$ matrix and B is a $\fbox{$2$}$ by $4$ matrix. The product $AB$ is defined, and is a $2$ by $4$ matrix. $AB=$ $\left[\begin{array}{llll} (4)(-6)+(1)(2) & (4)(6)+(1)(5) & (4)(1)+(1)(4) & (4)(0)+(1)(-1)\\ (2)(-6)+(1)(2) & (2)(6)+(1)(5) & (2)(1)+(1)(4) & (2)(0)+(1)(-1) \end{array}\right]$ $=\left[\begin{array}{cccc} {-22}&{29}&{8}&{-1}\\ {-10}&{17}&{6}&{-1}\end{array}\right]$
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