Answer
$\begin{bmatrix}1&-1&-1&|&10\\2&1&2&|&-1\\-3&4&0&|&5\\4&-5&1&|&0\end{bmatrix}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
x-y-z=10\\
2x+y+2z=-1\\
-3x+4y=5\\
4x-5y+z=0\end{cases}$
The general form of the system is:
$\begin{cases}
a_1x+b_1y+c_1z=d_1\\
a_2x+b_2y+c_2z=d_2\\
a_3x+b_3y+c_3z=d_3\\
a_4x+b_4y+c_4z=d_4\end{cases}$
The corresponding augmented matrix is:
$\begin{bmatrix} a_1&b_1&c_1&|&d_1\\a_2&b_2&c_2&|&d_2\\a_3&b_3&c_3&|&d_3\\a_4&b_4&c_4&|&d_4\end{bmatrix}$
The augmented matrix for the given system is:
$\begin{bmatrix}1&-1&-1&|&10\\2&1&2&|&-1\\-3&4&0&|&5\\4&-5&1&|&0\end{bmatrix}$
