# Chapter 11 - Systems of Equations and Inequalities - 11.2 Systems of Linear Equations: Matrices - 11.2 Assess Your Understanding - Page 730: 18

$\begin{bmatrix}1&-1&2&-1&|&5\\1&3&-4&2&|&2\\3&-1&-5&-1&|&-1\end{bmatrix}$

#### Work Step by Step

We are given the system of equations: $\begin{cases} x-y+2z-w=5\\ x+3y-4z+2w=2\\ 3x-y-5z-w=-1\end{cases}$ The general form of the system is: $\begin{cases} a_1x+b_1y+c_1z+d_1w=e_1\\ a_2x+b_2y+c_2z+d_2w=e_2\\ a_3x+b_3y+c_3z+d_3w=e_3\end{cases}$ The corresponding augmented matrix is: $\begin{bmatrix} a_1&b_1&c_1&d_1&|&e_1\\a_2&b_2&c_2&d_2&|&e_2\\a_3&b_3&c_3&d_3&|&e_3\end{bmatrix}$ The augmented matrix for the given system is: $\begin{bmatrix}1&-1&2&-1&|&5\\1&3&-4&2&|&2\\3&-1&-5&-1&|&-1\end{bmatrix}$

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