Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 4 - Section 4.2 - Matrix Multiplication - Exercises - Page 252: 19

Answer

$\left[\begin{array}{rr} 0 & 0\\ 0 & 0 \end{array}\right]$

Work Step by Step

If $A$ is an $m\times\boxed{n }$ matrix and $B$ is an $\boxed{n }\times k$ matrix, then the product $AB$ is the $m\times k$ matrix whose $ij-$th entry is the product $(AB)_{ij}=[a_{i1}\ a_{i2}\ a_{i3}\ \ldots\ a_{in}]\left[\begin{array}{l} b_{1j}\\ b_{2j}\\ b_{3j}\\ \vdots\\ b_{nj} \end{array}\right]$ $=a_{i1}b_{1j}+a_{i2}b_{2j}+a_{i3}b_{3j}+\cdots+a_{in}b_{nj}$. ------- Here, A is a $2\times 2$ matrix, B is a $2\times 2$ matrix AB is defined, and is a $2\times 2$ matrix. $AB=\left[\begin{array}{ll} 1(2)-1(2) & 1(3)-1(3)\\ 1(2)-1(2) & 1(3)-1(3) \end{array}\right]$ $=\left[\begin{array}{rr} 0 & 0\\ 0 & 0 \end{array}\right]$
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