If p = a₁ + a₁x + a₂x² and q = bo + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) =< p, q>= aobo + a₁b₁ + a₂b₂ Investigate whether: a. = (symmetry) b. < (p+q),r>=+ (additive) c. = k < p, q> (homogeneous) d. < p,p>≥ 0 with < p,p>= 0 if and only if p = 0 (positive)

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A: We can solve the given problem as follows:

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A: I am attaching image so that you understand each and every step.

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