Let Pn be the vector space of all polynomials of degree n or less in the variable x. Let D²: P4→P2 be the linear transformation that takes a polynomial to its second derivative. That is, D²(p(x))=p″(x) for any polynomial p(x) of degree 4 or less.
(a) Find a basis for the kernel of D².
(b) Find a basis for the image of D².