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 - 2.3 The Inverse of a Matrix - 2.3 Exercises - Page 71: 36


$$A^{-1}=-\frac{36}{143}\left[ \begin {array}{cccccc} \frac{8}{9}&-\frac{9}{4}\\ -\frac{5}{3}&-\frac{1}{4}\end {array} \right].$$

Work Step by Step

Since $ad-bc=-\frac{1}{4}\frac{8}{9}-\frac{9}{4}\frac{5}{3}=-\frac{143}{36}\neq 0$, then $A$ has inverse given by $$A^{-1}=-\frac{36}{143}\left[ \begin {array}{cccccc} \frac{8}{9}&-\frac{9}{4}\\ -\frac{5}{3}&-\frac{1}{4}\end {array} \right].$$
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