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: 25



Work Step by Step

We are given the augmented matrix: $\begin{bmatrix}5&-3&1&|&-2\\2&-5&6&|&-2\\-4&1&4&|&6\end{bmatrix}$ Write the system of equations corresponding to the given augmented matrix: $\begin{cases} 5x-3y+z=-2\\ 2x-5y+6z=-2\\ -4x+y+4z=6 \end{cases}$ Perform the row operation: $R_1=-2r_2+r_1$ $\begin{bmatrix}-2(2)+5&-2(-5)-3&-2(6)+1&|&-2(-2)-2\\2&-5&6&|&-2\\-4&1&4&|&6\end{bmatrix}$ $\begin{bmatrix}1&7&-11&|&2\\2&-5&6&|&-2\\-4&1&4&|&6\end{bmatrix}$ $R_3=2r_2+r_3$ $\begin{bmatrix}1&7&-11&|&2\\2&-5&6&|&-2\\2(2)-4&2(-5)+1&2(6)+4&|&2(-2)+6\end{bmatrix}$ $=\begin{bmatrix}1&7&-11&|&2\\2&-5&6&|&-2\\0&-9&16&|&2\end{bmatrix}$
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.