Use the definition of an inner product to determine which of the following defines an inner product on the indicated space. Verify your answers. ui a. (u, v) = u1vi – Uzvl – u1v2 + 3u2v2 for u = and v = u2 in R? V2 b. (f, g) = f'(0)g(0) for f,g € D(-1,1) (where D(a, b) is the vector space of all differentiible functions on the interval (a, b)) c. (u, v) = (Au)(Av) for u, v E R" and A is invertible n x n matrix.

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