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: 21



Work Step by Step

We are given the augmented matrix: $\begin{bmatrix}1&-3&4&|&3\\3&-5&6&|&6\\-5&3&4&|&6\end{bmatrix}$ Write the system of equations corresponding to the given augmented matrix: $\begin{cases} x-3y+4z=3\\ 3x-5y+6z=6\\ -5x+3x+4z=6 \end{cases}$ Perform the row operation: $R_2=-3r_1+r_2$ $\begin{bmatrix}1&-3&4&|&3\\-3(1)+3&-3(-3)-5&-3(4)+6&|&-3(3)+6\\-5&3&4&|&6\end{bmatrix}$ $=\begin{bmatrix}1&-3&4&|&3\\0&4&-6&|&-3\\-5&3&4&|&6\end{bmatrix}$ $R_3=5r_1+r_3$ $\begin{bmatrix}1&-3&4&|&3\\0&4&-6&|&-3\\5(1)-5&5(-3)+3&5(4)+4&|&5(3)+6\end{bmatrix}$ $=\begin{bmatrix}1&-3&4&|&3\\0&4&-6&|&-3\\0&-12&24&|&21\end{bmatrix}$
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