Hello mathematicians :)

I have a problem finding the inverse of the following 12x12 matrix:

C:=Matrix([

[ 1, x1, y1,    x1^2, x1*y1, y1^2,      x1^3,    x1^2*y1, x1*y1^2,   y1^3,      x1^3*y1,   x1*y1^3],
[ 0,  0,  1,       0,    x1, 2*y1,         0,      ...