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So I ran into an case I have not seen before. Say we have a system of 3 equations such that W´=AW, where W=(x(t),y(t),z(t)) and A is a 3x3 matrix. The way I usually approach these is by finding the eigenvalues of A to then find the eigenvectors and thus find the ¨homogenous¨ solution. What happens when the eigenvector I am looking for, given by a eigenvalue, is the null vector?

An example where this happens: A=(-1,0,1//2,-1,1//0,0,-1)

An example where this happens: A=(-1,0,1//2,-1,1//0,0,-1)

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