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 731: 26



Work Step by Step

We are given the augmented matrix: $\begin{bmatrix}4&-3&-1&|&2\\3&-5&2&|&6\\-3&-6&4&|&6\end{bmatrix}$ Write the system of equations corresponding to the given augmented matrix: $\begin{cases} 4x-3y-z=2\\ 3x-5y+2z=6\\ -3x-6y+4z=6 \end{cases}$ Perform the row operation: $R_1=-r_2+r_1$ $\begin{bmatrix}-3+4&-(-5)-3&-2-1&|&-6+2\\3&-5&2&|&6\\-3&-6&4&|&6\end{bmatrix}$ $\begin{bmatrix}1&2&-3&|&-4\\3&-5&2&|&6\\-3&-6&4&|&6\end{bmatrix}$ $R_3=r_2+r_3$ $\begin{bmatrix}1&2&-3&|&-4\\3&-5&2&|&6\\3-3&-5-6&2+4&|&6+6\end{bmatrix}$ $=\begin{bmatrix}1&2&-3&|&-4\\3&-5&2&|&6\\0&-11&6&|&12\end{bmatrix}$
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