Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 3 Linear Systems and Matrices - 3.8 Use Inverse Matrices to Solve Linear Systems - 3.8 Exercises - Skill Practice - Page 214: 6


$$ \begin{pmatrix}-1&-3\\ \frac{2}{3}&\frac{7}{3}\end{pmatrix}$$

Work Step by Step

We know the following equation for the inverse of a matrix: $$\begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}^{-1}=\frac{1}{\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}}\begin{pmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{pmatrix}$$ Thus: $$\frac{1}{\det \begin{pmatrix}-7&-9\\ 2&3\end{pmatrix}}\begin{pmatrix}3&-\left(-9\right)\\ -2&-7\end{pmatrix} \\ \begin{pmatrix}-1&-3\\ \frac{2}{3}&\frac{7}{3}\end{pmatrix}$$
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