Algebra and Trigonometry 10th Edition

Published by Cengage Learning

Chapter 10 - 10.3 - The Inverse of a Square Matrix - 10.3 Exercises - Page 734: 14

Answer

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

Work Step by Step

We need to augment the matrix by adding the Identity Matrix $\begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}$ Therefore, $\begin{bmatrix} 1& 2& 1 & 0 \\ 3& 7& 0 & 1\end{bmatrix}$ Now, multiply row $1$ by $-3$ and add it to row $2$ We have : $\begin{bmatrix} 1 & 0 & 7 &-2 \\ 0 & 1 &3 &-1\end{bmatrix}$ Our answer is: $\begin{bmatrix} 7 &-2 \\ 3 &-1\end{bmatrix}$

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