Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 2 - Matrices - 2.4 Elementary Matrices - 2.4 Exercises - Page 82: 18

Answer

$$\left[ \begin {array}{cccccc} \frac{1}{5}&0\\ 0&1\end {array} \right].$$

Work Step by Step

Since $ad-bc=(5)(1)-(0)(0)=5\neq 0$, then the matrix has inverse given by $$ \frac{1}{5} \left[ \begin {array}{cccccc} 1&0\\ 0&5\end {array} \right]=\left[ \begin {array}{cccccc} \frac{1}{5}&0\\ 0&1\end {array} \right].$$
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