For the following functions, justify why they are NOT inner products on the indicated vector space....

 

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For the following functions, justify why they are NOT inner products on the indicated vector space. (a) On R, define (x, y) = xy + x2x3Y2Y3, where x = (x1, x2, x3) and = (y, Y2, Y3). (b) On P2, define (p(x), g(x)) = p(1)q(1). (For example, if p(x) = x - 2x = P, then plug in x = 1 to get p(1) = 1 2(1) = 1.) - (c) On M2,2, define (A, B) = det(A) det (B). - For the following functions, justify why they are NOT inner products on the indicated vector space. (a) On R, define (x, y) = xy + x2x3Y2Y3, where x = (x1, x2, x3) and = (y, Y2, Y3). (b) On P2, define (p(x), g(x)) = p(1)q(1). (For example, if p(x) = x - 2x = P, then plug in x = 1 to get p(1) = 1 2(1) = 1.) - (c) On M2,2, define (A, B) = det(A) det (B). -

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