The original matrix           A row echelon form        The rref of the matrix

[-1    1     1    0    -1]  [-1    1     1     0      -1]  [1    0    0    0     3]
[                        ]  [                           ]  [                      ]
[ 2    0     0    1     2]  [ 0    2     2     1       0]  [0    1    0    0     2]
[                        ], [                           ], [                      ]
[ 2    0    -1    1     2]  [ 0    0    -1     0       0]  [0    0    1    0     0]
[                        ]  [                           ]  [                      ]
[-1    2    -1    0     1]  [ 0    0     0    -1/2     2]  [0    0    0    1    -4]