Question: Thank you! Problem 4. Let Pr(x] denote the vector space of polynomials of degree at most n over F: Pa[x]- {ao taiIt ... + and

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Problem 4. Let Pr(x] denote the vector space of polynomials of degree at most n over F: Pa[x]- {ao taiIt ... + and" | a; (F). Consider the following function V : P2(x] X P3(x] > Ps[x] (f,g) fg. (a) Prove that I is bilinear. (b) By (a), I induces a linear map T : P2(x] @ Par] + Ps(x] such that T(f @ g) = fg. (You do not have to show that T is linear - this comes from the definition of the tensor product!) Compute the standard matrix of T with respect to the bases {1, r, x} C P2(x], {1, x, x2, x3) ( Pax] and {1, x, 1', 13, ra, x ] CPs[x]. Hint: first write a basis for Pz[x]

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