Is it possible to solve a variable inside a matrix? Like an Eigenvalue problem where the determinant of a matrix should be equal to zero and a variable is to be solved inside the matrix.

I can't do it in Prime (limited by Express), but here's how to do it (Using Mathcad 11), Prime should be similar.

Your problem is like:

Then to solve for omega:

Success!
Luc

on the other side, results:

So, what is the solution? Who knows?

Luc showed one way and this seems to answer your question about solving for a variable used in a matrix.

It uses Mathcads symbolics because using a numeric solve block would only give you one solution, depending on a guess value.

For your specific example you could also use the built-in function "genvals".

Anyway I get quite the same results as Luc and they differ from the values given in your picture!??