Linear Algebra -- More Spanning Sets

Solving problems on spanning sets

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...d, ii) means a contradiction i.e. if x(k+1) is independent, then there are members of V that require x(k+1). But by definition, we have all of the elements necessary to obtain ALL of the members of V through linear combination. So either we are contradicting the fact that (x1...xk) is a spanning set of V or that x(k+1) is ...