# Chapter 3 Linear Systems and Matrices - 3.8 Use Inverse Matrices to Solve Linear Systems - 3.8 Exercises - Skill Practice - Page 214: 11

The student multiplied by the determinant instead of dividing by the determinant.

#### 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: $$\frac{1}{\det \begin{pmatrix}2&4\\ 1&5\end{pmatrix}}\begin{pmatrix}5&-4\\ -1&2\end{pmatrix} \\ \begin{pmatrix}\frac{5}{6}&-\frac{2}{3}\\ -\frac{1}{6}&\frac{1}{3}\end{pmatrix}$$

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