Consider the map T: P P given by (a) Calculate T(x - x) = (b)...

 

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Consider the map T: P₂ → P₁ given by (a) Calculate T(x - x²) = (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 Otherwise leave the following spaces blank. p(x) = q(x) = T(a + a₁x + a₂x²) = 2a + a₂ -2a₁x. (d) Does T preserve scalar multiplication? If not, enter a scalar k and polynomial r E P₂ such that Otherwise leave the following spaces blank. and r(x) = k = (e) Is T a linear transformation? T(p+q) T(p) + T(q). T(kr) #kT(r). Consider the map T: P₂ → P₁ given by (a) Calculate T(x - x²) = (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 Otherwise leave the following spaces blank. p(x) = q(x) = T(a + a₁x + a₂x²) = 2a + a₂ -2a₁x. (d) Does T preserve scalar multiplication? If not, enter a scalar k and polynomial r E P₂ such that Otherwise leave the following spaces blank. and r(x) = k = (e) Is T a linear transformation? T(p+q) T(p) + T(q). T(kr) #kT(r).