Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 10 - 10.3 - The Inverse of a Square Matrix - 10.3 Exercises - Page 734: 18

Answer

$\begin{bmatrix} 1 & 1 \\ 3 & 4 \end{bmatrix}$

Work Step by Step

The general form of a matrix of order $ 2 \times 2$ is: $Det \ A \begin{bmatrix} p & q \\ r & s\end{bmatrix}=ps-qr$ Write the augmented matrix with identity matrix. $\begin{bmatrix}1 & -1/4 \\ 0 & 1/4 \end{bmatrix} $ Now, add row $2$ to row $1$, then multiply row $2$ by $4$. $\begin{bmatrix} 1 & 1 \\ 3 & 4 \end{bmatrix}$ Our answer is: $\begin{bmatrix} 1 & 1 \\ 3 & 4 \end{bmatrix}$
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