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Let S={u,v,w}S={u,v,w} be a linearly independent set in a vector space V. Prove that the set...

Let S={u,v,w}S={u,v,w} be a linearly independent set in a vector space V. Prove that the set S′={3u−w,v+w,−2w}S′={3u−w,v+w,−2w} is also a linearly independent set in V.

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