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: 8

Answer

The product is not defined

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 1$\times$2 matrix, B is a 1$\times$2 matrix AB is not defined because the number of rows in B does not equal the number of columns in A The product is not defined.
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