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: 6

Answer

$[-5x+y]$

Work Step by Step

If $A$ is an $m\times n$ matrix and $B$ is an $n\times k$ matrix, then the product $AB$ is the $m\times k$ matrix whose $ij-$th entry is the product $(AB)_{ij}=[a_{i1}\ a_{i2}\ a_{i3}\ \ldots\ a_{in}]\left[\begin{array}{l} b_{1j}\\ b_{2j}\\ b_{3j}\\ \vdots\\ b_{nj} \end{array}\right]$ $=a_{i1}b_{1j}+a_{i2}b_{2j}+a_{i3}b_{3j}+\cdots+a_{in}b_{nj}$. ------- A is a 1$\times$3 matrix, B is a 3$\times$1 matrix AB is defined and is a 1$\times$1 matrix $AB_{11}=4(-x)-1(x)+1(y)=-5x+y$ $AB=[-5x+y]$
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