(3 points) Consider the map T: P₂ → P₁ given by (a) Calculate T(x² - 2x) = (b) Give an example of a non-zero polynomial

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3 Points Consider The Map T P P Given By A Calculate T X 2x B Give An Example Of A Non Zero Polynomial 1 (28.85 KiB) Viewed 39 times

(3 points) Consider the map T: P₂ → P₁ given by (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(z) = P₂ such that Otherwise leave the following spaces blank. p(x) = q(z) = (d) Does T preserve scalar multiplication?? If not, enter a scalar k and polynomial r = P₂ such that Otherwise leave the following spaces blank. k= and r(x) = (e) Is T a linear transformation?? T(ao + a₁ + a₂x²) = 3a + a₂ + a₁x. T(p+q) T(p) + T(q). T(kr) #kT(r).