5. Let V be a vector space (note that this is an arbitrary vector space - not necessarily F"). Suppose dim(V) = n. Prove that a set of vectors {v₁,..., Vn} in V is linearly independent if and only if it spans V. Hint 1: Remember (from sec. 1.6) that there is always an isomorphism A: V → F and isomorphisms "preserve" bases (and so preserves linear independence). Hint 2: Think in terms of pivots.

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Q: 14. What are the conditions on a set of vectors S to be a basis for a vector space V?

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Q: prove that T= S.

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Q: 3c

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