Deteminate of a 12x12 symbolic matrix is equal to zero while it shouldn't

I am trying to solve an eigenvalue problet in which i have to find the determinate of 12x12 symbolic matrix and then solve the equation to find the eigenvalues

every time itry to find the determinate using the det() function i have det(K) = 0 while it shouldn't.

[Walter Roberson]

Are most of the entries of the symbolic matrix 0? Because the general det() of a 12x12 symbolic matrix would have about 479 million terms.

Are the terms symbolic variables? Symbolic rationals? Symbolic floating point numbers?

syms x
[x, sym(73)/49, sym(73/49, 'd')]

ans = 

Symbolic floating point numbers have the same kind of problems that regular flointing point numbers do, with issues having to do with rounding, and cancellation of terms.

[Mohammad Al-Bakry]

Yes it is a stiffness matrix

[Walter Roberson]

Knowing that it is a stiffness matrix does not tell me what kind of values are in it, or how many zeros there are.

What shows up for rank() of the matrix ?

[Mohammad Al-Bakry]

I want to solve for P

here is a snapshot of whati it looks like

the rank = 10

[Walter Roberson]

rank 10 on a 12x12 matrix guarantees determinant 0.

[Mohammad Al-Bakry]

Is there any other method to solve for the determinate?

[Walter Roberson]

[V,D] = eig(K)

The determinant of K is prod(diag(D)). D will have two 0 values on the diagonal and 10 non-zero values, so the determinant will be 0.