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

Let U, V and W be finite dimensional real vector spaces, T: U> V, S ; V-W and P : W>U be linear transformations. f range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is true ? (A) nulity of T = nlity 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