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

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