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Problem 3. Let A E M9((C), with eigenvalues A,a and \"y with algebraic multiplicity 4, 2 and 3 and geometric multiplicities 2, 1 and 1 respectively. (1) We say two Jordan forms are equivalent if they only differ by the order of the Jordan blocks. Give all possible nonequivalent Jordan canonical forms for A with the given information. (2) Moreover suppose we know rank(A AI)3 = rank(A AI)4 and rank(A AI)2 a rank(A AI)3. Give all nonequivalent possible Jordan canonical forms for A with the given information. (3) Suppose a Jordan canonical form of a linear transformation T, written in the Jordan basis 8 = {51,"' 735} is where '7 and CM are distinct scalars. Which of the sets below is a linearly independent subset of C5? Justify. _' _. (a) {3\"(b4)LT(323),b2} (b) {airings} (C) {b41T(b4)1b3}