Problem 2 Let T : C'(-1, 1) -> C(-1, 1) be defined as: (Tf ) (t ) = df (t ) dt - af(t) , Vte (-1, 1) where a E R is given and fixed and with the usual internal and external operations for real valued functions. 1. Find the kernel, the nullity and the rank of 7 (Hint: for nullity and rank, remember the theorem relating their dimensions). 2. Prove that the subset W = {f : (-1, 1) -> R|f(0) = 0} is a subspace of Cl(-1, 1) and find the kernel of T : W -> W (we will use this exercise later for linear systems of ordinary differential equations)