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: 24



Work Step by Step

We are given the augmented matrix: $\begin{bmatrix}1&-3&-4&|&-6\\6&-5&6&|&-6\\-1&1&4&|&6\end{bmatrix}$ Write the system of equations corresponding to the given augmented matrix: $\begin{cases} x-3y-4z=-6\\ 6x-5y+6z=-6\\ -x+y+4z=6 \end{cases}$ Perform the row operation: $R_2=-6r_1+r_2$ $\begin{bmatrix}1&-3&-4&|&-6\\-6(1)+6&-6(-3)-5&-6(-4)+6&|&-6(-6)-6\\-1&1&4&|&6\end{bmatrix}$ $=\begin{bmatrix}1&-3&-4&|&-6\\0&13&30&|&30\\-1&1&4&|&6\end{bmatrix}$ $R_3=r_1+r_3$ $\begin{bmatrix}1&-3&-4&|&-6\\0&13&30&|&30\\1-1&-3+1&-4+4&|&-6+6\end{bmatrix}$ $=\begin{bmatrix}1&-3&-4&|&-6\\0&13&30&|&30\\0&-2&0&|&0\end{bmatrix}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.