Answer to Question #44642 in Linear Algebra for Anurodh

Question

Let V be the vector space of polynomials 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.