Problem 5 Let S₁ and S₂ be subsets of a vector space V. Prove the followings: (1) span (S₁) span(S₂). (2) span (S₁ S₂) span(S₁) span (S₂). Give an example in which span(S₁ S₂) and span (S₁) span (S₂) are equal and one in which they are unequal. (3) span (S₁ US₂2) = span (S₁) + span(S₂).

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