EXERCISES 1. Let the linear mapping g : L → M of finite-dimensional spaces be associated with the...
Problem 5. Let W and U be finite-dimensional vector spaces, and let T : W > W and S : W -> U be linear transformations. Prove that if rank(S o T) L W W such that S o T = So L. = rank(S), then there exists an isomorphism (,.. . , Vk) is a basis of ker(T), and let (w1, ., wr) is a basis of im(T) nker(S) if 1 ik Hint: Let B (vi,... , Vk,...,vj,) be...