Question: Suppose that V is a finite-dimensional vector space and T : V V is a linear function. (a) Suppose that T T = T. Show

Suppose that V is a finite-dimensional vector space and T : V V is a linear function. (a) Suppose that T T = T. Show that V = ker(T) im(T). (b) Give an example to show that if T T /= T then it can happen that V /= ker(T) im(T). (/= means not equal)

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