Homework #5 for 445
Due: Feb 24, 2006
Read Chapter 4 of Meerschaert
Exercises from the text (Meerschaert)
1. Section 4.4, Problem 5
2. Review the solution methods for the following problems by outlining the solution approach
and solving part c) in detail.
a) Give the steps in the procedure for finding the eigenvalues and eigenvectors for the n × n
matrix A. That is, describe how you would find the non-trivial solutions to the problem
(A − λI) u = 0.
(Note u and λ are both vectors of length n)
b) Show how you would use the result from part a) to solve the problem
du
= Au
dt
.
c) Find the solution to parts a) and b) for
A=
.
"
−4 −1
3
0
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