uitgewerkt
$
\begin{array}{l}
\left( {\begin{array}{*{20}c}
{\left. {\begin{array}{*{20}c}
1 & 1 & 1 & 0 \\
2 & { - 2} & { - 5} & 0 \\
3 & 0 & 1 & 1 \\
4 & { - 2} & { - 3} & 1 \\
\end{array}} \right|} & {\begin{array}{*{20}c}
6 \\
{ - 13} \\
{13} \\
1 \\
\end{array}} \\
\end{array}} \right) \\
R2 - 2R1 \to R2 \\
R3 - 3R1 \to R3 \\
R4 - 4R1 \to R4 \\
\left( {\begin{array}{*{20}c}
{\left. {\begin{array}{*{20}c}
1 & 1 & 1 & 0 \\
0 & { - 4} & { - 7} & 0 \\
0 & { - 3} & { - 2} & 1 \\
0 & { - 6} & { - 7} & 1 \\
\end{array}} \right|} & {\begin{array}{*{20}c}
6 \\
{ - 25} \\
{ - 5} \\
{ - 23} \\
\end{array}} \\
\end{array}} \right) \\
4R3 - 3R2 \to R3 \\
2R4 - 3R2 \to R4 \\
\left( {\begin{array}{*{20}c}
{\left. {\begin{array}{*{20}c}
1 & 1 & 1 & 0 \\
0 & { - 4} & { - 7} & 0 \\
0 & 0 & {13} & 4 \\
0 & 0 & 7 & 2 \\
\end{array}} \right|} & {\begin{array}{*{20}c}
6 \\
{ - 25} \\
{55} \\
{29} \\
\end{array}} \\
\end{array}} \right) \\
13R4 - 7R3 \to R4 \\
\left( {\begin{array}{*{20}c}
{\left. {\begin{array}{*{20}c}
1 & 1 & 1 & 0 \\
0 & { - 4} & { - 7} & 0 \\
0 & 0 & {13} & 4 \\
0 & 0 & 0 & { - 2} \\
\end{array}} \right|} & {\begin{array}{*{20}c}
6 \\
{ - 25} \\
{55} \\
{ - 8} \\
\end{array}} \\
\end{array}} \right) \\
\left( {\begin{array}{*{20}c}
{\left. {\begin{array}{*{20}c}
1 & 1 & 1 & 0 \\
0 & { - 4} & { - 7} & 0 \\
0 & 0 & {13} & 4 \\
0 & 0 & 0 & 1 \\
\end{array}} \right|} & {\begin{array}{*{20}c}
6 \\
{ - 25} \\
{55} \\
4 \\
\end{array}} \\
\end{array}} \right) \\
\left( {\begin{array}{*{20}c}
{\left. {\begin{array}{*{20}c}
1 & 1 & 1 & 0 \\
0 & { - 4} & { - 7} & 0 \\
0 & 0 & {13} & 0 \\
0 & 0 & 0 & 1 \\
\end{array}} \right|} & {\begin{array}{*{20}c}
6 \\
{ - 25} \\
{39} \\
4 \\
\end{array}} \\
\end{array}} \right) \\
\left( {\begin{array}{*{20}c}
{\left. {\begin{array}{*{20}c}
1 & 1 & 1 & 0 \\
0 & { - 4} & { - 7} & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{array}} \right|} & {\begin{array}{*{20}c}
6 \\
{ - 25} \\
3 \\
4 \\
\end{array}} \\
\end{array}} \right) \\
\left( {\begin{array}{*{20}c}
{\left. {\begin{array}{*{20}c}
1 & 1 & 1 & 0 \\
0 & { - 4} & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{array}} \right|} & {\begin{array}{*{20}c}
6 \\
{ - 4} \\
3 \\
4 \\
\end{array}} \\
\end{array}} \right) \\
\left( {\begin{array}{*{20}c}
{\left. {\begin{array}{*{20}c}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{array}} \right|} & {\begin{array}{*{20}c}
2 \\
1 \\
3 \\
4 \\
\end{array}} \\
\end{array}} \right) \\
\end{array}
$