Let T be a linear transformation such that T : V V . (a) If V = R 2 , can image(T) = ker(T)? If so, provide an example. If not, justify with a proof. (b) If V = R 3 , can image(T) = ker(T)? If so, provide an example. If not, justify with a proof. These two example hint at a general condition for finite dimensional vector spaces that must be true in order image(T) = ker(T). Prove that if this condition holds a linear transformation does exist such that image(T) = ker(T)