(3 points) Consider the map T: P2 → P₁ given by T(a₁ + a₁x + a₂x²) = 3αo + ª₂ + ª₁x. (a) Calculate T(x² – 2x) = = (b) Gi

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(3 points) Consider the map T: P2 → P₁ given by T(a₁ + a₁x + a₂x²) = 3αo + ª₂ + ª₁x. (a) Calculate T(x² – 2x) = = (b) Give an example of a non-zero polynomial p(x) = P₂ so that T (p(x)) = 0 p(x) = (c) Does T preserve vector addition? ? If not, enter two polynomials p(x), q(x) = P₂ such that T(p+q) T(p) +T(q). Otherwise leave the following spaces blank. p(x) = q(x) = (d) Does T preserve scalar multiplication? ? If not, enter a scalar k and polynomial r = P₂ such that T(kr) kT(r). Otherwise leave the following spaces blank. k= and r(x) - (e) Is T a linear transformation? ? =