(Exercises by P. Anthappan) 1. Dene the eigenvalue and eigenvector of a square matrix A. 1 2 2. What are the eigenvalues of the matrix A = [ 1 4] . Find the corresponding eigenvectors. 4 2 2 3. What are the eigenvalues of the matrix A = 2 4 2 . Find the corresponding eigenvectors. 2 2 4 4. Show that if a matrix is invertible, and DL at 0 is an eigenvalue of A, then i is an eigenvalue of A-l. 1 1 2 5. Show that J? =[1] is an eigenvector of A = [ 1 4]