Answer
\[ \left[\begin{array}{rrr|r} 2 & 3 & -4 & 0 \\ 1 & 0 & -5 & -2 \\ 1& 2 &-3 & -2 \\ \end{array} \right] \]
Work Step by Step
I modify the original equations in the form such that the constant "goes" onto the other side of the equality.
$x-5z+2=0\\x-5z=-2$
We know that \[ \left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \\ \end{array} \right. \] becomes \[ \left[\begin{array}{rrr|r} a_1 & b_1 & c_1 & d_1 \\ a_2 & b_2 & c_2 & d_2 \\ a_3 & b_3 & c_3 & d_3 \\ \end{array} \right] \] Hence here the augmented matrix is: \[ \left[\begin{array}{rrr|r} 2 & 3 & -4 & 0 \\ 1 & 0 & -5 & -2 \\ 1& 2 &-3 & -2 \\ \end{array} \right] \]
