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: 69

Answer

Two matrices are subtracted by subtraction of corresponding elements, but only when they are of the same order.

Work Step by Step

Two matrices can be subtracted only if they have the same dimensions, that is, two matrices must have the same numbers of rows and columns (that is, the order of matrices should be the same). If they are of different orders, there would be a minimum of one extra row or column in one of the matrices and subtraction would not be possible. Example: Consider two matrices of the 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 subtraction operation on 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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