Consider the map T: P2 → P1 given by T(ao + aj x + az x²) = -ao – a2 – 2aj x. (a) Calculate T(2x – 1) = (b) Give an example of a non-zero polynomial p(x) E P2 so that T (p(x)) = 0 p(x) = (c) Does T preserve vector addition? ? If not, enter two polynomials p(x), q(x) E P2 such that T(p + q) + T(p) + T(q). Otherwise leave the following spaces blank. = (x)d q(x) = (d) Does T preserve scalar multiplication? ? If not, enter a scalar k and polynomial r e P2 such that T(kr) + kT(r). Otherwise leave the following spaces blank. k = and r(x) = (e) Is T a linear transformation? ?

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