Suppose V is a finite dimensional vector space and that L: V V is a...

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Suppose V is a finite dimensional vector space and that L: V → V is a linear operator that satisfies L(L()) = L(T) for all & EV. (a) Show that A = 0 and X = 1 are the only possibilities for the eigenvalues of L. (b) Prove that L is diagonalizable. Suppose V is a finite dimensional vector space and that L: V → V is a linear operator that satisfies L(L()) = L(T) for all & EV. (a) Show that A = 0 and X = 1 are the only possibilities for the eigenvalues of L. (b) Prove that L is diagonalizable.

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