Let P2 denote the vector space of all polynomials with real coefcients and of degree at most 2. Dene a function T : P2 gt; P; by d2 d T(p(w)) www)...

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2. Let P2 denote the vector space of all polynomials with real coefficients and of degree at most 2. Define a function T : P2 —> P; by d2 dT(p(w)) — wwflw) + Qfiflw), for all p(m) E P2. In addition, let 5' = (1, m, .132) be the standard basis of P2. (a) Show that T : P2 —> P2 is a linear operator.(b) Find the matrix A for which [T(p(3:))]3 = A [p(:1:)]3 for all 19(37) E P2.