4. The operator T: Q4 Q4 has (with respect to the standard basis) the matrix 2 0 07 10 0 2 1 0 A = 0 020 0 -1 0 2 and has characteristic polynomial XT(x) = (x-2)4. (a) Find the minimal polynomial of T. (b) Find the Jordan normal form of T. (c) Find a Jordan basis of Q4 for T. (d) Find the rational canonical form of T. (e) Find a rational canonical basis for T.

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