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Let B be a (finite) basis for a vector space V. Suppose that v is a...

Let B be a (finite) basis for a vector space V. Suppose that v is a vector in V but not in B. Prove that, if we enlarge B by adding v to it, we get a set that cannot possibly be a basis for V. (We have not yet formally defined dimension, so don't use that idea in your proof.)

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