(3) Let V be an inner product space, and suppose v1, ..., vn eV is a...

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(3) Let V be an inner product space, and suppose v1, ..., vn eV is a spanning set, that is Span(v1, ..., vn) = V. Suppose that u1, u2 € V are vectors such that (u1, vi) = (u2, vi) for 1 ≤ i ≤ n. Show that u1 = u2 Hint: You may want to start with showing that (u1-u2, v) = 0 for every V EV. (3) Let V be an inner product space, and suppose v1, ..., vn eV is a spanning set, that is Span(v1, ..., vn) = V. Suppose that u1, u2 € V are vectors such that (u1, vi) = (u2, vi) for 1 ≤ i ≤ n. Show that u1 = u2 Hint: You may want to start with showing that (u1-u2, v) = 0 for every V EV.

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