Prove that the map T: P2 M 2x2 (R) defined by T (p (x)) =...

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Prove that the map T: P2 → M 2x2 (R) defined by T (p (x)) = [a 0 a 10 a 2 ] for each p(x) = a0 + a 1x + a 2x2 in P2 is a linear transformation. If D C M 2 x 2 (R) is the subspace of M 2 x 2 (R) consisting of all 2 × 2 diagonal matrices, what is the preimage T-1 (D) of the set D ? (Note: Given T: V → W, the preimage of a set DC W under T is the set T-1 (D) = {vEV:T(v) ED}. Your answer to the second part should involve a description of a certain subset of polynomials from P 2) Prove that the map T: P2 → M 2x2 (R) defined by T (p (x)) = [a 0 a 10 a 2 ] for each p(x) = a0 + a 1x + a 2x2 in P2 is a linear transformation. If D C M 2 x 2 (R) is the subspace of M 2 x 2 (R) consisting of all 2 × 2 diagonal matrices, what is the preimage T-1 (D) of the set D ? (Note: Given T: V → W, the preimage of a set DC W under T is the set T-1 (D) = {vEV:T(v) ED}. Your answer to the second part should involve a description of a certain subset of polynomials from P 2)

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