Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 11 - Systems of Equations and Inequalities - Chapter Review - Review Exercises - Page 794: 17


$\begin{bmatrix} \dfrac{1}{2}&-1\\-\dfrac{1}{6}&\dfrac{2}{3}\end{bmatrix}$

Work Step by Step

We are given the matrix: $A=\begin{bmatrix}4&6\\1&3\end{bmatrix}$ In order to compute $A^{-1}$ use the formula: $A^{-1}=\dfrac{1}{det A}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}$ where $A=\begin{bmatrix}a&b\\c&d\end{bmatrix}$ and $det A=ad-bc$. First compute $detA$: $detA=4(3)-1(6)=6\not=0$ As $detA\not=0$, the inverse of $A$ exists. Determine $A^{-1}$: $A^{-1}=\dfrac{1}{6}\begin{bmatrix} 3&-6\\-1&4\end{bmatrix}=\begin{bmatrix} \dfrac{1}{2}&-1\\-\dfrac{1}{6}&\dfrac{2}{3}\end{bmatrix}$
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