Question: 3. V be a vector space over a field F, and let U be a subspace of V with U not equal to {0}. Suppose

3. V be a vector space over a field F, and let U be a subspace of V with U not equal to {0}. Suppose that is a basis for V . Is it necessarily true that there is some such that is a basis for U? If so, prove it. If not, give an explicit counterexample.

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