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: 8

Answer

$$\begin{pmatrix}-\frac{5}{36}&-\frac{11}{72}\\ -\frac{1}{12}&-\frac{1}{24}\end{pmatrix}$$

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: $$ \frac{1}{\det \begin{pmatrix}6&-22\\ -12&20\end{pmatrix}}\begin{pmatrix}20&-\left(-22\right)\\ -\left(-12\right)&6\end{pmatrix} \\ \begin{pmatrix}-\frac{5}{36}&-\frac{11}{72}\\ -\frac{1}{12}&-\frac{1}{24}\end{pmatrix}$$
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