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

[-1     1     2    -1    0]  [-1     1     2    -1    0]  [1    0    0    0    7/12]
[                         ]  [                         ]  [                        ]
[-1     0     1     2    1]  [ 0    -1    -1     3    1]  [0    1    0    0    3/4 ]
[                         ], [                         ], [                        ]
[ 1     0    -1     1    1]  [ 0     0     4     0    1]  [0    0    1    0    1/4 ]
[                         ]  [                         ]  [                        ]
[ 1    -1     2     1    1]  [ 0     0     0     3    2]  [0    0    0    1    2/3 ]