Math 603-601 - Fall 2002

Assignment 7

1. Find the eigenvalues and eigenvectors of the matrices below. Determine whether or not a given matrix is diagonalizable. If it is, find S for which S^-1AS=D.

    3  4        2  1 
   -1 -1       -1  2 
   

2. Bring the quadratic form Q(X) = 4x² + 4y² + 4z² - 2xy + 2xz - 2yz into diagonal form. Find a set of principal axes.

3. Find the normal modes of a horizontal spring system attached to wall mounts and consisting of three springs (constants = k, 3k, k) and two identical masses (mass = m).