Still not clear what you are looking for.
You are talking of 5 different homogenous systems (depending on which component of omega you use) and the solution would be trivially the null vector in any case !
A homogenous system always will have either the null vector as its only solution, or there is an infinite number of solutions depending on one ore more parameters.
Why do you think that Phi15=1 ?
BTW, do you have a problem with the caps lock key on your computer?
File is an older file in Mathcad 15 format.
In Prime go to the Input/Output ribbon tab.
There is an xmcd,mcd converter button.
Press this button and you can add files for prime to convert.
The file has a sample using genval and genvect to solve for frequencies and mode shapes.