6. (Section 5.4) Let T: P2P be the linear transformation that maps a polynomial p(x) to the polynomial p(x) + 2p(z) (a) If p(z) = 2 + 3x-x2, then what is T(p)? (b) Find the matrix for T relative to the bases {1,2,22} and {1,z,?2,23,24). (c) Write the polynomial from part (a) as a vector in R2 and use the matrix from (b) to verify your answer to part (a).
Show transcribed image text6. (Section 5.4) Let T: P2P be the linear transformation that maps a polynomial p(x) to the polynomial p(x) + 2p(z) (a) If p(z) = 2 + 3x-x2, then what is T(p)? (b) Find the matrix for T relative to the bases {1,2,22} and {1,z,?2,23,24). (c) Write the polynomial from part (a) as a vector in R2 and use the matrix from (b) to verify your answer to part (a).