College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 6 - Matrices and Determinants - Exercise Set 6.4 - Page 639: 27

Answer

$\begin{bmatrix}1&0&0&0&|&1&0&0&0\\0&1&0&0&|&0&-1&0&0\\0&0&1&0&|&0&0&\dfrac{1}{3}&0\\0&0&0&1&|&-1&0&0&1\end{bmatrix}$

Work Step by Step

We are given the matrix: $A=\begin{bmatrix}1&0&0&0\\0&-1&0&0\\0&0&3&0\\1&0&0&1\end{bmatrix}$ We start with the matrix: $\begin{bmatrix}1&0&0&0&|&1&0&0&0\\0&-1&0&0&|&0&1&0&0\\0&0&3&0&|&0&0&1&0\\1&0&0&1&|&0&0&0&1\end{bmatrix}$ Add $-R_1$ to $R_4$: $\begin{bmatrix}1&0&0&0&|&1&0&0&0\\0&-1&0&0&|&0&1&0&0\\0&0&3&0&|&0&0&1&0\\0&0&0&1&|&-1&0&0&1\end{bmatrix}$ Multiply $R_2$ by -1: $\begin{bmatrix}1&0&0&0&|&1&0&0&0\\0&1&0&0&|&0&-1&0&0\\0&0&3&0&|&0&0&1&0\\0&0&0&1&|&-1&0&0&1\end{bmatrix}$ Multiply $R_3$ by $\dfrac{1}{3}$: $\begin{bmatrix}1&0&0&0&|&1&0&0&0\\0&1&0&0&|&0&-1&0&0\\0&0&1&0&|&0&0&\dfrac{1}{3}&0\\0&0&0&1&|&-1&0&0&1\end{bmatrix}$
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