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 - 11.2 Systems of Linear Equations: Matrices - 11.2 Assess Your Understanding - Page 730: 23



Work Step by Step

We are given the augmented matrix: $\begin{bmatrix}1&-3&2&|&-6\\2&-5&3&|&-4\\-3&-6&4&|&6\end{bmatrix}$ Write the system of equations corresponding to the given augmented matrix: $\begin{cases} x-3y+2z=-6\\ 2x-5y+3z=-4\\ -3x-6x+4z=6 \end{cases}$ Perform the row operation: $R_2=-2r_1+r_2$ $\begin{bmatrix}1&-3&2&|&-6\\-2(1)+2&-2(-3)-5&-2(2)+3&|&-2(-6)-4\\-3&-6&4&|&6\end{bmatrix}$ $=\begin{bmatrix}1&-3&2&|&-6\\0&1&-1&|&8\\-3&-6&4&|&6\end{bmatrix}$ $R_3=3r_1+r_3$ $\begin{bmatrix}1&-3&2&|&-6\\0&1&-1&|&8\\3(1)-3&3(-3)-6&3(2)+4&|&3(-6)+6\end{bmatrix}$ $=\begin{bmatrix}1&-3&2&|&-6\\0&1&-1&|&8\\0&-15&10&|&-12\end{bmatrix}$
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