Maybe I misunderstand what you are trying to do, but the way I read it is that you set lambda="rhs expression", and substitute that into the matrix on the lhs, which yields the matrix on the rhs. The problem is, such a substitution will not result in the matrix on the rhs. Initially I thought all your diagonal terms were wrong, but in fact all terms other than the zeros are wrong. If that's what you are trying to do, anyway 
. If not, you need to explain in more detail the steps you are taking and why you think the solutions(s) are wrong.
The third method needs a value for m.1 and the assignment := instead of = for omega.1 as shown.
The first method has three equations and only two unknowns. The m.1's all cancel. Put the omega.1 variable back in and solve for it too.
It found 6 solutions.
