(a) Determine whether the following are inner products on the given vector space V. (Either show that all the inner product axioms are satisfied, or give an example to show that some inner product axiom fails.) i) Let V be a real vector space of dimension 3 and B be a basis for V. For u, v E V, define (u, v) = [u]A[v] B where ii) Let V = R2 and define A = 2 1 0 1 1 0 0 04 ((x1, x2), (y₁, y2)) = 2x1y₁ +5x1y2 + 5x2Y1 + x2Y2

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