Let V be a vector space over a field F. Let B1 {v1, v2} and B2 = {w1, w2, w3} be linearly independent sets of vectors in V. Assume that none of v1, v2, w1, w2, W3 are equal to each other, they are all distinct vectors. Prove that if span(ß1) N span(B2) # 0 then B1 U B2 is a linearly dependent set.

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