i am a little stuck becuase there is so many concepts at once. i know what each of things are by the definitions, but to put them together, i'm not sure of the idea. here is the problem "let p(n) be the real vector space denoting the polynomial functions up to degree n. consider the linear transformation D(f) = d/dx (f). give a basis for the kernel of D. also, what is the rank of the linear transformation D?". now, I know kernel means, once you apply the LT, you get zero. so its the functions where the derivative is zero. but does this mean, for example, all the cooeficcients are zero? or that the whole function goes? so only the constant term, so the basis would just be 1?. i have mostly done vector spaces of matrixes, not really polynomials so i dont know if the rules apply"