I have a system of matrices to solve for a,b,c,d

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I have to use numerical methods NOT analytical methods, that means I can't just multiply it out and solve for a,b,c,d simultaneously. An numerical method would be something like making an original guess for a,b,c,d and using an algorithm to find better estimates and repeating the algorithm until my estimates are accurate much like the Newton-Raphson iteration does. In reality the matrices are 18x20 and 1x18 but I scaled down the problem to be more manageable.