# Given 3x3 matrix M (individual rows add up to 1) find a 3x1 vector v such that v=Mv.

Given a 3x3 matrix M whose individual rows add up to 1 find a 3x1 vector v (not all zero) such that v=Mv. (Hint: Do a few examples.)

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The trivial answer would be M=I, the identity matrix and v is any vector, but that would be too easy, and therefore rejected as a solution.

If v = Mv, then M has 1 as an eigenvalue and v is the ...

#### Solution Summary

Given a 3x3 matrix M whose individual rows add up to 1, a 3x1 vector v (not all zero) such that v=Mv is found. Please note that the solution is not the identity vector. The solution is detailed and well presented.

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