# Chapter 11 - Systems of Equations and Inequalities - 11.2 Systems of Linear Equations: Matrices - 11.2 Assess Your Understanding - Page 731: 25

$\begin{bmatrix}1&7&-11&|&2\\2&-5&6&|&-2\\0&-9&16&|&2\end{bmatrix}$

#### 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: $R_1=-2r_2+r_1$ $\begin{bmatrix}-2(2)+5&-2(-5)-3&-2(6)+1&|&-2(-2)-2\\2&-5&6&|&-2\\-4&1&4&|&6\end{bmatrix}$ $\begin{bmatrix}1&7&-11&|&2\\2&-5&6&|&-2\\-4&1&4&|&6\end{bmatrix}$ $R_3=2r_2+r_3$ $\begin{bmatrix}1&7&-11&|&2\\2&-5&6&|&-2\\2(2)-4&2(-5)+1&2(6)+4&|&2(-2)+6\end{bmatrix}$ $=\begin{bmatrix}1&7&-11&|&2\\2&-5&6&|&-2\\0&-9&16&|&2\end{bmatrix}$

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