SYST 611 Homework #1

Issued: September 3, 2009  Due:  September 10, 2009

Notes

• The material we covered the first half of the class is from Chapter 1 of Luenberger.
• An explanation of eigenvalues and eigenvectors can be found on page 77 ff. of Luenberger.
• Partial fraction expansions (the method of partial fractions) is explained on page 83 ff. of the Schaum's Outline Series book
• Partial fraction expansions are also discussed in Luenberger page 263-266

Four questions, equal weight.

1.  Assuming that x(0) = 0, x(1) = 1, find the next four terms x(2), x(3), x(4), and x(5) using the difference equation

2. [Hint: see Luenberger, chapter 3 or----use Google!]

    For the matrix

        (a) Find the characteristic polynomial

        (b) Find its determinant and trace

        (c) Find its eigenvalues

        (d) Find the eigenvectors associated with the eigenvalues found in part (c)

3. Using the method of partial fractions, find the partial fraction expansion of:

4.  Consider

(a) Find the value of A³⁰

(b) Find the value of e^At

Use the techniques discussed in class.  Show your work.