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Can this underdetermined equation be solved?

Mathematics Asked by LoneWolf on November 6, 2021

We have the following equation p=(1+s)p(A+dl) where p is an unknown vector, d as well as l are given vectors, s a constant and A a diagonal matrix. Would it be possible to solve this equation without an extra one? Or is it simply underdetermined?
Could it be solved with a Perron-Frobenius eigenvalue?
Thank you in advance.

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