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 919: 68


Two matrices are added by adding the corresponding elements and only if they are of the same order.

Work Step by Step

Two matrices can be added by adding the corresponding elements only if they have the same numbers of rows and columns (the orders must match) If they are of different orders, there would be a minimum of one extra row or column in one of the matrices. Example: Consider two matrices of order $2\times 2$: $A=\left( \begin{matrix} a & b \\ c & d \\ \end{matrix} \right)$ and $B=\left( \begin{matrix} e & f \\ g & h \\ \end{matrix} \right)$ Then, the addition operation on the matrices is performed as follows: $\begin{align} & A+B=\left( \begin{matrix} a & b \\ c & d \\ \end{matrix} \right)+\left( \begin{matrix} e & f \\ g & h \\ \end{matrix} \right) \\ & =\left( \begin{matrix} a+e & b+f \\ c+g & d+h \\ \end{matrix} \right) \end{align}$
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