Suppose TV V is a linear transformation from V to V and {v,..., Um} is a basis of T(V). Let 3 = {w,..., wm} CV such that T(w;) = v; and W = span{3}. Show that V = WN(T), i.e., each v V can be written uniquely as v = w + u where we W, u = N(T). Here N(T) = {x E VIT(x) = 0} is the null space. v