Question: Decide if the following statements are TRUE or FALSE. Write a proof for the true nes and provide a counter-example for the rest. Every

Decide if the following statements are TRUE or FALSE. Write a proof

Decide if the following statements are TRUE or FALSE. Write a proof for the true nes and provide a counter-example for the rest. Every linear operator T: R" R" can be written as T = D+N, where D is diagonalizable, N is nilpotent and DN = ND.

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