zojr Let T: V > W be a linear transformation from an n-dimensional vector space V to an m-dimensional vector space W. Let B and 7 be ordered bases for V and W, respectively. Prove that rank(T) = rank(LA) and that nullity(T) : nullity(LA), where A = [T]; Hint: Apply Exercise 17 to Figure 2.2. E.g., show that N(T) is preserved under these transformations TOY (\\phi_g T (N(t)) = 0 and L_A \\phi_b (N(T)) = 0, and I guess there are no other sets in V to do that Also show that RYT) is preserved, that is ( Vo ) L_A \\phi_b(V) = \\phi_g T(V) (which is that theorem 2.21 with the diagram, so should be easy to point to it) 0/10