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