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Suppose that V is finite dimensional and let T : V - V be a linear map such that T2 = T. 1. Prove that

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Suppose that V is finite dimensional and let T : V - V be a linear map such that T2 = T. 1. Prove that V = Image(T) ker (T). 2. Given an example to show that this is not always possible when V is an infinite dimensional vector space

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