use Math::MatrixLUP;
my @planes3D = (
  [1, 2, 1, -1], # ax+by+cz+n=0
  [2, 3, -2, 2]
);
print Math::MatrixLUP->new(\@planes3D)->rref
# says
# [1, 0, -7, 7],
# [0, 1, 4, -4]