Question: Question 1 (25 points) Let p(X) 2 X3 + 2X2 + 7X 2 E (:[X]. Find the characteristic polynomial of A E (C8X8 knowing that

Question 1 (25 points) Let p(X) 2 X3 + 2X2 + 7X 2 E (:[X]. Find the characteristic polynomial of A E (C8X8 knowing that the following three conditions hold: 0 mA(X) 2 (X2 1)(X2 4). o tr(p(A)) 2 18. o dimker(A Id) 2 2. 0 There are no linearly independent vectors 11,10 in C8 such that p(A)v 2 121) and p(A)w 2 1210

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