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: 35


$$A^{-1}=\frac{20}{59}\left[ \begin {array}{cccccc} \frac{4}{5}&\frac{3}{4}\\ -\frac{1}{5}&\frac{7}{2}\end {array} \right].$$

Work Step by Step

Since $ad-bc=\frac{7}{2}\frac{4}{5}+\frac{3}{4}\frac{1}{5}=\frac{59}{20}\neq 0$, then $A$ has inverse given by $$A^{-1}=\frac{20}{59}\left[ \begin {array}{cccccc} \frac{4}{5}&\frac{3}{4}\\ -\frac{1}{5}&\frac{7}{2}\end {array} \right].$$
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