# Chapter 8 - Section 8.4 - Matrix Algebra - 8.4 Assess Your Understanding - Page 598: 25

$\left[\begin{array}{rrrr} {-2}&{4}&{2}&{8}\\ {2}&{1}&{4}&{6}\end{array}\right]$

#### 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. $AB=\\\left[\begin{array}{llll} 2(2)+(-2)(3) & 2(1)+(-2)(-1) & 2(4)+(-2)(3) & 2(6)+(-2)(2)\\ 1(2)+(0)(3) & 1(1)+(0)(-1) & 1(4)+(0)(3) & 1(6)+(0)(2) \end{array}\right]$ $=\left[\begin{array}{rrrr} {-2}&{4}&{2}&{8}\\ {2}&{1}&{4}&{6}\end{array}\right]$

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