reduced-row-echelon-form.java returns wrong result

[axkr]

The reduced-row-echelon-form.java of this example:

  double[][] matrix_0 = {
    {1,0,-1,0},
    {0,1,0,-1},
    {1,-2,-1,0},
    {-1,0,3,1}
  };

  Matrix x = new Matrix(matrix_0);
  System.out.println("before\n" + x.toString() + "\n");
  x.RREF();
  System.out.println("after\n" + x.toString() + "\n");

should return the 4x4 identity matrix.

See wolframalpha for the input:

RowReduce({{1,0,-1,0},{0,1,0,-1},{1,-2,-1,0},{-1,0,3,1}})