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: 29


$\left[\begin{array}{cc} {9}&{2}\\ {34}&{13}\\ {47}&{20}\end{array}\right]$

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 $3$ by $\fbox{$3$}$ matrix and B is a $\fbox{$3$}$ by $2$ matrix. The product $AB$ is defined, and is a $3$ by $2$ matrix. $AB=\left[\begin{array}{ll} {1(1)+0(6)+1(8)}&{1(3)+0(2)+1(-1)}\\ {2(1)+4(6)+1(8)}&{2(3)+4(2)+1(-1)}\\ {3(1)+6(6)+1(8)}&{3(3)+6(2)+1(-1)}\end{array}\right]$ $=\left[\begin{array}{cc} {9}&{2}\\ {34}&{13}\\ {47}&{20}\end{array}\right]$
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