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QUESTION
Suppose that {v1, v2, ., vn} is linearly independent set of vectors in a vector space V and that w is another vector in V . Prove that if {v1 + w,...
Suppose that {v1, v2, ...., vn} is linearly independent set of vectors in a vector space V and that w is another vector in V . Prove that if {v1 + w, v2+,...., vn+w} is linearly dependent then w ∈ span(v1, v2,...., vn).
