Question: Problems finding the inverse of an algebraic 12x12 matrix

Hello mathematicians :)

I have a problem finding the inverse of the following 12x12 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.


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