Question: Let p(X) = X + 2X +7X 2 C[X]. Find the characteristic polynomial of A C88 knowing that the following three conditions hold: mA(X)

Let p(X) = X + 2X +7X 2 C[X]. Find the characteristic polynomial of A C88 knowing that the following three conditions hold: mA(X) = (X2 1)(X24). tr (p(A)) = 18. dim ker (A - Id) = 2. . There are no linearly independent vectors v, w in C8 such that p(A)v = 12v and p(A)w = 12w.

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