Let u, v and w be finite dimensional real vector spaces, t:u> v,s : v> w and p: w+u be linear transformations. if range (st) = nullspace (p), nullspace (st) = r

Let U, V and W be finite dimensional real vector spaces, T:U> V,S : V> W and P: W+U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank(T) = rank(S), then which one of the following is TRUE? (A) nullity of T = nullity of S (B) dimension of U # dimension of W (C)If dimension of V =3, dimension of U = 4, then P is not identically zero (D) If dimension of V =4, dimension of U = 3 and T is one-one, then P is identically zero