Answer Happy

Please solve a and b.
We define the following function between polynomial vector spaces. A:Pd + Pd+1 a1 The map A takes in a polynomial and produces a new polynomial with the rule ao +212 + ... +adze 67 002 + 47.22 + ... + d+1 Now, consider another function ad_24+1 D:P + Pd-1 which is given by the rule 20 +ajr+ ... + adrd 6a+222 + ... +aded-1. a. (4 pnts) Are these linear maps? If so, compute their matrices with respect to monomial bases for d=4. To be specific, that's the basis where 00 ai p(x) = [1 ad (1) ad So you would need to compute one matrix A for the function A so that A multiplied by the coefficient vector [az], (d + 1) 1 is the column vector with the output polynomial's coefficients. Then do the same with a matrix D for the function D. b. (4 pnts) Are A and D invertible? If so, what are their inverses? If not, why not?