Okey, this is only half programming, but let's see how you are on terms with manual calculations. I believe many of you did this on your university's while giving "linear systems" ... the problem is it's been so long I can't remember how to do it any more.

I know quite a few algorithms for calculating determinants, and they all work fine ... for large systems, where one would never try to do it manually. Unfortunatelly, I'm soon going on an exam, where I do have to calculate it manually, up to the system of 5.

So, I have a K(omega) matrix that looks like this:

[2-(omega^2)*c       -4       2       0       0]  
[-2       5-(omega^2)*c      -4       1       0]  
[1       -4       6-(omega^2)*c      -4       1]  
[0        1      -4       5-(omega^2)*c      -2]  
[0        0       2      -4       2-(omega^2)*c]  

and I need all the omegas which satisfy the det[K(omega)]=0 criteria.

What would be a good way to calculate it so it can be repeated in a manual process ?