Question: Please prove without using Rank-Nullity Theorem. Just basic injection, subjection, and duality with linear transformation. Let V/K be a vector space, let ( C V

Please prove without using Rank-Nullity Theorem. Just basic injection, subjection, and duality with linear transformation.

Let V/K be a vector space, let ( C V be a subspace, and let T : V - W be a surjective linear transformation. Assume dim U + dim W > dim V. Prove there exists u E ( such that

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