The standard basis for P2 x is l xx2 The standard basis for

The standard basis for P_2 (x) is {l, x,x^2}. The standard basis for P_2(x) is {l, x, x^2, x^3} Find the standard matrix representation for the linear map T_2: P_2(x) rightarrow P_3(x) given by T_2(p(x)) Find the standard matrix representation for the linear map D_3: P_3(x) rightarrow P_2(X) where D_3(p(x)) = dp(x)/dx The composition of D_3ocy T_2. P_2(x) rightarrow P_2(x) is a linear map find its matrix representation using the standard basis Find the matrix representation using the standard basis for T-2 D_3: P_3(x) rightarrow P_3(x)

Solution

P2 (x) = {1,x,x²}

P3 (x) = {1,x,x²,x³}