(4) (3 Points) True for False: If TV →→W is a linear transformation between subspaces V, W of R" and V₁, V2, ..., Vk € V are linearly independent then T(v₁), T(V₂), ..., T(Vk) € W are lin- early independent. Please provide justification or a counterexample. O (a) True (b) False (5) (3 Points) True for False: For any n x n matrix A, if there exists a nonzero vector x ER" such that Ax = x then 1 is an eigenvalue of A.