A={{1,-1/2,0,-1},{-1/3,1,-1/2,0},{-1/3,0,1,0},{-1/3,-1/2,-1/2,1}}
RowReduce[A]

B={{1, -2, 4, 9}, {1,-1, 2, 5}, {3,-5, 13,32}}
RowReduce[B]