Hello I have this system: $$ x'=2kx + ky + kz, y'=kx+ 2ky + kz, z'=kx+ ky+ 2kz $$. I found that λ=k and 4k. I am solving for the first eigenvector when λ=k, and end up with this: a+b+c=0, can anyone help how to put this expression into eigenvector matrix? I will solve for the second lambda and the have the general solution for the system, and its known that x(0)=1, y(0)=0, z(0)=0. Thanks for help, I have just started solving systems so I got confused..
2026-04-01 15:36:59.1775057819
Solving a system of 3 DE's. Need a tip for finding eigenvecotr
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