Question: Let {u, v, w} be a linearly independent set of vectors in a vector space V. (a) Is {u + v, v + w, u

Let {u, v, w} be a linearly independent set of vectors in a vector space V.
(a) Is {u + v, v + w, u + w} linearly independent? Either prove that it is or give a counterexample to show that it is not.
(b) Is {u - v, v - w, u - w} linearly independent? Either prove that it is or give a counterexample to show that it is not.

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a Yes it is Suppose au v bv w cu w a cu a bv b cw 0 Since u v w are linearly indepen... View full answer

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