Let u be an eigenvector of A corresponding to an eigenvalue A, and let H be the

Question:

Let u be an eigenvector of A corresponding to an eigenvalue A, and let H be the line in Rn through u and the origin.
a. Explain why H is invariant under A in the sense that Ax is in H whenever x is in H.
b. Let K be a one-dimensional subspace of Rn that is invariant under A. Explain why K contains an eigenvector of A.