Answer to Question #40911 in Linear Algebra for asjad

Question

let v be the vector space of polynomial with real coefficients and of degree at most 2. If D=d/dx is the differential operator on v and B={1+2x^2, x+x^2, x^2} is an ordered basis of V, find [D]b. find the rank and nullity of D. Is D invertible? justify your answer.