Gauso metodas 2.1a.
$\left(\begin{array}{rrr|r}1 &-1 &-3 &0 \\2 &1 &1 &4 \\1 &1 &2 &3\end{array}\right)$
$\left.\begin{array}{c}\; \\\leftarrow \\\leftarrow \end{array}\right.\sim$
$\left(\begin{array}{rrr|r}1 &-1 &-3 &0 \\1 &1 &2 &3 \\2 &1 &1 &4\end{array}\right)$
$\left.\begin{array}{c}\;\times\text{(-1)} \\\leftarrow \text{+} \\\;\end{array}\right.\sim$
$\left(\begin{array}{rrr|r}1 &-1 &-3 &0 \\0 &2 &5 &3 \\2 &1 &1 &4\end{array}\right)$
$\left.\begin{array}{c}\;\times\text{(-2)} \\\; \\\leftarrow \text{+} \end{array}\right.\sim$
$\sim\left(\begin{array}{rrr|r}1 &-1 &-3 &0 \\0 &2 &5 &3 \\0 &3 &7 &4\end{array}\right)$
$\left.\begin{array}{c}\; \\\leftarrow \text{+} \\\;\times\text{(-1)}\end{array}\right.\sim$
$\left(\begin{array}{rrr|r}1 &-1 &-3 &0 \\0 &-1 &-2 &-1 \\0 &3 &7 &4\end{array}\right)$
$\left.\begin{array}{c}\; \\\;\times\text{3} \\\leftarrow \text{+} \end{array}\right.\sim$
$\left(\begin{array}{rrr|r}1 &-1 &-3 &0 \\0 &-1 &-2 &-1 \\0 &0 &1 &1\end{array}\right)$
$\left.\begin{array}{c}\; \\\leftarrow \text{+} \\\;\times\text{2}\end{array}\right.\sim$
$\sim\left(\begin{array}{rrr|r}1 &-1 &-3 &0 \\0 &-1 &0 &1 \\0 &0 &1 &1\end{array}\right)$
$\left.\begin{array}{c}\leftarrow \text{+} \\\; \\\;\times\text{3}\end{array}\right.\sim$
$\left(\begin{array}{rrr|r}1 &-1 &0 &3 \\0 &-1 &0 &1 \\0 &0 &1 &1\end{array}\right)$
$\left.\begin{array}{c}\leftarrow \text{+} \\\;\times\text{(-1)} \\\;\end{array}\right.\sim$
$\left(\begin{array}{rrr|r}1 &0 &0 &2 \\0 &-1 &0 &1 \\0 &0 &1 &1\end{array}\right)$
$\left.\begin{array}{c}\; \\|\cdot(-1) \\\;\end{array}\right.\sim$
$\sim\left(\begin{array}{rrr|r}1 &0 &0 &2 \\0 &1 &0 &-1 \\0 &0 &1 &1\end{array}\right)$
; $X=\begin{bmatrix}2 \\-1 \\1\end{bmatrix}.$