Question: 2. Decide if the following statement is True or False: Let V be a vector space over C, and let Te C(V) have characteristic polynomial

2. Decide if the following statement is True or False: Let V be a vector space over C, and let Te C(V) have characteristic polynomial (A+ 1)(1+ 2)3. If T is not diagonalizable, then there exists a vector x E V such that (7 + 2/)3x = 0 but (T + 2/)-x /0. Indicate your final answer by filling in exactly one circle below (unfilled O filled .) and justify your choice with a proof or counter-example. [4 marks] O True O False

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