Answer
$x_1=1,$ $x_2=-1,$ $x_3=2,$ $x_4=0,$ $x_5=-2,$ $x_6=1$
Work Step by Step
The augmented matrix is
$\left[ {\begin{array}{*{20}{c}}
1&2&{ - 2}&2&{ - 1}&3\\
2&{ - 1}&3&1&{ - 3}&2\\
1&3&{ - 2}&1&{ - 2}&{ - 3}\\
3&{ - 2}&1&{ - 1}&3&{ - 2}\\
{ - 1}&{ - 2}&1&2&{ - 2}&3\\
1&{ - 3}&1&3&{ - 2}&1
\end{array}\left| {\begin{array}{*{20}{c}}
0\\
{17}\\
{ - 5}\\
{ - 1}\\
{10}\\
{11}
\end{array}} \right.} \right]$
By using MATLAB software, the row reduced echelon form is
$\left[ {\begin{array}{*{20}{c}}
1&0&0&0&0&0\\
0&1&0&0&0&0\\
0&0&1&0&0&0\\
0&0&0&1&0&0\\
0&0&0&0&1&0\\
0&0&0&0&0&1
\end{array}\left| {\begin{array}{*{20}{c}}
1\\
{ - 1}\\
2\\
0\\
{ - 2}\\
1
\end{array}} \right.} \right]$
Hence, the solution is given by
$x_1=1,$ $x_2=-1,$ $x_3=2,$ $x_4=0,$ $x_5=-2,$ $x_6=1$
