Question (1) Given a vector space V with dim V = n, along with a spanning set S = {v1,... , vk} for V with k > n, explain how to find a subset B of S that is a basis for V. Illustrate this procedure in the case V = P2(F), with the set of vectors {2x2 - x +3, x2 + 2, 3.x – 1, -a2 + 2x, 4.x2 + 4x +4}.

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