Finite Math and Applied Calculus (6th Edition)

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

Chapter 4 - Section 4.1 - Matrix Addition and Scalar Multiplication - Exercises - Page 241: 54

Answer

$A-B$ is a $ 2\times 3$ matrix with all entries equal to zero.

Work Step by Step

If$ A$ and $B$ are $m\times n$ matrices, then $A-B$ is the $m\times n$ matrix whose entries are given by: $(A-B)_{ij}=A_{ij}-B_{ij}$ ijth entry of the difference $=$ difference of the ijth entries ------- Since $A=B$, it follows that $A_{ij}=B_{ij},$ so $(A-B)_{ij}=A_{ij}-B_{ij}=0$ $A-B$ is a $ 2\times 3$ matrix with all entries equal to zero.
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