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, x1^2, 2*x1*y1, 3*y1^2, x1^3, 3*x1*y1^2],
[ 0, -1, 0, (-2)*x1, -y1, 0, (-3)*x1^2, (-2)*x1*y1, -y1^2, 0, (-3)*x1^2*y1, -y1^3],
[ 1, x2, y2, x2^2, x2*y2, y2^2, x2^3, x2^2*y2, x2*y2^2, y2^3, x2^3*y2, x2*y2^3],
[ 0, 0, 1, 0, x2, 2*y2, 0, x2^2, 2*x2*y2, 3*y2^2, x2^3, 3*x2*y2^2],
[ 0, -1, 0, (-2)*x2, -y2, 0, (-3)*x2^2, (-2)*x2*y2, -y2^2, 0, (-3)*x2^2*y2, -y2^3],
[ 1, x3, y3, x3^2, x3*y3, y3^2, x3^3, x3^2*y3, x3*y3^2, y3^3, x3^3*y3, x3*y3^3],
[ 0, 0, 1, 0, x3, 2*y3, 0, x3^2, 2*x3*y3, 3*y3^2, x3^3, 3*x3*y3^2],
[ 0, -1, 0, (-2)*x3, -y3, 0, (-3)*x3^2, (-2)*x3*y3, -y3^2, 0, (-3)*x3^2*y3, -y3^3],
[ 1, x4, y4, x4^2, x4*y4, y4^2, x4^3, x4^2*y4, x4*y4^2, y4^3, x4^3*y4, x4*y4^3],
[ 0, 0, 1, 0, x4, 2*y4, 0, x4^2, 2*x4*y4, 3*y4^2, x4^3, 3*x4*y4^2],
[ 0, -1, 0, (-2)*x4, -y4, 0, (-3)*x4^2, (-2)*x4*y4, -y4^2, 0, (-3)*x4^2*y4, -y4^3]
]);
I have tried solving it in MATLAB, with no succes (used up all 12GB ram after calculating for two days!), and now it seems, that I have the same problem in MAPLE. Is that matrix really that insane to find the inverse of ?
Anyways, can you guys give me advice on a workaround to find the solution? I need the solution to be algebraic, since the matrix is gonna be used repeatedly with different values for x1, x2, x3, x4, y1, y2, y3, y4, and I don't want to insert the values before inverting since it makes my MATLAB program very slow!
I really hope you guys can help me out here.
Thanks in advance.
Kind regards
Dennis Thogersen, Denmark.
