MATH 557, Fall 2007, Homework set # 7 , Due: October 22, 2007
1. Prove from the definition of similarity that
·2 1
−0 2 ¸and ·2 0
−0 2 ¸
are not similar.
2. Find out how to obtain eigenvalues and eigenvectors of a matrix in MATLAB
(Try >>help eig). Using MATLAB as much as possible, find a fundamental matrix
for y0=Aywhere
A=
4−5 0 3
0 4 −3−5
5−3 4 0
3 0 5 4
(Remark: MATLAB provides normalized eigenvectors. You may find it easier to
multiply by a convenient factor to get a non-normalized form.)
3. Work problem 9, page 105 of the text in its entirety.