Question: (13 points) Given vectors u, v in R, show that they are linearly independent if and only if the vectors u+v and u-v are

(13 points) Given vectors u, v in R", show that they are linearly independent if and only if the vectors u+v and u-v are linearly independent. (12 points) Suppose that vectors u, v, w in R" satisfy Span({u, v, w}) = Span({u, v}) Is it true that vectors u, v, w must be linearly dependent? If no, construct a counterex- ample, if yes, prove it.

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