Question: 1. Let f : R -> R be a function with the property that for any v, w C R it holds that f (v)

1. Let f : R" -> R" be a function with the property that for any v, w C R" it holds that f (v) . f (w) = v .w. I.e. f preserves the inner product on the vector space R". Show that f is a linear transfor- mation

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