Exercise 4.13 Consider the subspace 2 1 - ( ) ( ) ( ! ) 200 0 2 0 002 1 002 2 1 CM (3 × 3, R). 002 a) Determine the subset S of matrices of W admitting 2 as eigenvalue. Is S a subspace? Is it a linear variety? b) Determine which among the matrices of S are diagonalisable. c) Determine which among the matrices of S are similar to a Jordan matrix with a single block.

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