Question: (a) Suppose that A is a 3 x 3 matrix and that A, its only eigenvalue, has a geometric multiplicity of two. Let U(A, A)

(a) Suppose that A is a 3 x 3 matrix and that A, its only eigenvalue, has a geometric multiplicity of two. Let U(A, A) be the set U(A, A) = {u e R3 | (A Mm = v for some '0 e E(A, )0} where E(A, A) is the eigenspace of A for the eigenvalue A. Show that the following statements are true. (i) U(A, A) is a subspace of R3. (ii) E(A, A) Q U(A, A). (iii) E(A, A) 75 U(A, A). (b) Suppose that A is the matrix 0 2 1 A = 0 1 0 1 2 2 Find an invertible matrix P such that P'lAP = J where J is in Jordan normal form. Hence nd A'6 for k E N, simplifying your answer as far as possible

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