: 0.3 0 8. (13 points) Let A 0.2 0.1 0.4 0 0.4 0.1 (a) (3 points) Find the eigenvalues of A (b) (3 points) Find the eigenvectors associated with each eigenvalue of A. (e) (5 points) Diagonalize A, and use it to compute lim A k-oo (d) (2 points) Suppose A is an nxn matrix that is diagonalizable (so it has n linearly independent eigenvectors). What must be true for lim A to exist? What is k-oo needed for Ak 0? Justify your answer