(i) Let v, v' E V. Suppose that (vlr) = (vr) for every x V. Prove that v = v'. (ii) Suppose that S: V→W and T: W→ V are mappings that satisfies (Sv|w) = (v|Tw) (v EV, WEW) Note that the leff-hand side is the inner product in W (both Su and w are vectors in W), while the right-hand side is the inner product in V (both v and Tw are vectors in V). Prove that S is linear. 1

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