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Linear 2 step by step solution needed (a) Let A be a 6-by-6 matrix. Suppose that (A -/) =0. Suppose that the nullspace of (A

Linear 2 step by step solution needed

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(a) Let A be a 6-by-6 matrix. Suppose that (A -/) =0. Suppose that the nullspace of (A - I) has dimension 3. Write down the possibilities for the Jordan normal form of A. [6 marks] (b) Let A be an n-by-n matrix and let J = J,,(0). Suppose that AJ = JA. Prove that A = f(J) for some polynomial f. [6 marks]

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