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