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Suppose v1, v2, . . . , vn is linearly independent in V and w ∈...

Suppose v1, v2, . . . , vn is linearly independent in V and w ∈ V . Show that v1, v2, . . . , vn, w is linearly independent if and only if w ∈/ Span(v1, v2, . . . , vn).

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