Question: Let V be an inner product space. (a) Prove that (x. v) = 0 for all v V if and only if x =

Let V be an inner product space.
(a) Prove that (x. v) = 0 for all v € V if and only if x = 0.
(b) Prove that (x. v) = (y. v) for all v e V if and only if x = y.
(c) Let v1,...,vn be a basis for V. Prove that (x, v,) = (y, vj), i = 1,.... n, if and only if x = y.

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a Choosing v x we have 0 x x x 2 and hence x 0 b Rewrite the condition as 0 x v y v ... View full answer

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