Answer
$ \left\{\begin{array}{lllll}
x_{1} & & & +x_{4} & =-2\\
& x_{2} & & +2x_{4} & =2\\
& & x_{3} & -x_{4} & =0\\
& & & 0 & =0
\end{array}\right. $
The system is consistent. Solution set =
$\{(x_{1},x_{2},x_{3},x_{4})\ |\ x_{1}=-2-x_{4},\ \ x_{2}=2-2x_{4}\ \ x_{3}=x_{4}, \ \ x_{4} \in \mathbb{R} \}$
Work Step by Step
The system represented by the augmented matrix is
$ \left\{\begin{array}{lllll}
x_{1} & & & +x_{4} & =-2\\
& x_{2} & & +2x_{4} & =2\\
& & x_{3} & -x_{4} & =0\\
& & & 0 & =0
\end{array}\right. $
The last equation is always true. The system is consistent.
Take $x_{4}\in \mathbb{R}$, (any real number)
Equation 3 $\Rightarrow x_{3}=x_{4}$
Equation 2 $\Rightarrow x_{2}=2-2x_{4}$
Equation 1 $\Rightarrow x_{1}=-2-x_{4}$
Solution set =
$\{(x_{1},x_{2},x_{3},x_{4})\ |\ x_{1}=-2-x_{4},\ \ x_{2}=2-2x_{4}\ \ x_{3}=x_{4}, \ \ x_{4} \in \mathbb{R} \}$
