Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 8 - Section 8.3 - Matrix Operations and Their Applications - Exercise Set - Page 920: 77


The statement makes sense.

Work Step by Step

Two matrices can be added only if they have the same numbers of rows and columns. If they are of different orders, there would be a minimum of one extra row or column in one of the matrices; there would be no element in the other matrix to be added to the elements of that extra row or column. Consider the two matrices of order $2\times 2$ $A=\left( \begin{matrix} a & b \\ c & d \\ \end{matrix} \right)$ and $B=\left( \begin{matrix} e & f \\ g & h \\ \end{matrix} \right)$. The addition operation on the matrices is performed as follows: $\begin{align} & A+B=\left( \begin{matrix} a & b \\ c & d \\ \end{matrix} \right)+\left( \begin{matrix} e & f \\ g & h \\ \end{matrix} \right) \\ & =\left( \begin{matrix} a+e & b+f \\ c+g & d+h \\ \end{matrix} \right) \end{align}$ Therefore, the statement makes sense.
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