For each of the following inner product spaces V (over F) and linear transformations g: VF,...

 

 

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For each of the following inner product spaces V (over F) and linear transformations g: VF, find a vector y such that g(x) = (x, y) for all x E V. (a) VR, g(a1, a2, a3) = a12a2+4a3 (b) VC, g(21, 22) = 21-222 1 (c) V = P(R) with (f,h) = f(t)h(t) dt, g(f) = f(0) + f'(1) For each of the following inner product spaces V (over F) and linear transformations g: VF, find a vector y such that g(x) = (x, y) for all x E V. (a) VR, g(a1, a2, a3) = a12a2+4a3 (b) VC, g(21, 22) = 21-222 1 (c) V = P(R) with (f,h) = f(t)h(t) dt, g(f) = f(0) + f'(1)