[Q5] (Section 5.2: Eigenpairs and Subspaces; Related to Exercise 5.2.18) Let A e R be an eigenvalue of A e Roxn, and consider the associated eigenspace: Sx = {ve R" | Av = AU } CR", which consists of all eigenvectors of A associated with A, together with one additional vector: the zero vector. Show that Sx is actually a subspace of R", meaning that it is algebraically closed with respect to the usual vector space operations on I". (Hint: This is actually easy; just take an arbitrary linear combination of any two vectors from Sx, and show that any vector you get is always still in Sx.)