@acer Hi, thanks for getting back to me.

I have a system of 22 equations with 22 unknowns. I am working on solving a PDE for an euler bernoulli beam system. I took my 22-equation system and extracted the coefficients from each of my unknowns and represented that system as the matrix I described above. The system has cos, sin, sinh, and cosh terms involving omega as well as 2nd, 3rd, and 4th roots of omega.

I see I can attach documents so I will try and link my worksheet file.
Model_Derivation_2.mw