Answer
The system is inconsistent
Work Step by Step
$Ax=b$
$\begin{bmatrix}
1&-1&0 & -1\\
2 & 1 & 3 & 7\\
3 & -2 &1 & 0
\end{bmatrix}.\begin{bmatrix}
x_1\\
x_2\\
x_3
\end{bmatrix}=\begin{bmatrix}
2\\
2\\
4
\end{bmatrix}$
Converting the given system of equations to an augmented matrix and then using Gauss-Jordan elimination to determine the solution set to the given system.
$\begin{bmatrix}
1&-1&0 & -1|2\\
2 & 1 & 3 & 7|2\\
3 & -2 &1 & 0|4
\end{bmatrix} \approx^1\begin{bmatrix}
1&-1&0 & -1|2\\
0 & 3 & 3 & 9|-2\\
0 & 1 &1 & 3|-2
\end{bmatrix} \approx^2 \begin{bmatrix}
1&-1&0 & -1|2\\
0 & 1 & 1 & 3|-2\\
0 & 3 &3 & 9|-2
\end{bmatrix}\approx^3 \begin{bmatrix}
1&0&1 & 2|0\\
0 & 1 & 1 & 3|-2\\
0 & 0 &0 & 0|4
\end{bmatrix}$
1. $A_{12}(-2),A_{13}(-3)$
2. $P_{23}$
5. $A_{21}(1),A_{23}(-3)$
The system is inconsistent since $rank(A) \lt rank (A^\ne)$
