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