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: 22



Work Step by Step

We are given the augmented matrix: $\begin{bmatrix}1&-3&3&|&-5\\-4&-5&-3&|&-5\\-3&-2&4&|&6\end{bmatrix}$ Write the system of equations corresponding to the given augmented matrix: $\begin{cases} x-3y+3z=-5\\ -4x-5y-3z=-5\\ -3x-2x+4z=6 \end{cases}$ Perform the row operation: $R_2=4r_1+r_2$ $\begin{bmatrix}1&-3&3&|&-5\\4(1)-4&4(-3)-5&4(3)-3&|&4(-5)-5\\-3&-2&4&|&6\end{bmatrix}$ $=\begin{bmatrix}1&-3&3&|&-5\\0&-17&9&|&-25\\-3&-2&4&|&6\end{bmatrix}$ $R_3=3r_1+r_3$ $\begin{bmatrix}1&-3&3&|&-5\\0&-17&9&|&-25\\3(1)-3&3(-3)-2&3(3)+4&|&3(-5)+6\end{bmatrix}$ $=\begin{bmatrix}1&-3&3&|&-5\\0&-17&9&|&-25\\0&-11&13&|&-9\end{bmatrix}$
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