Unformatted text preview: ristic equation is Hence the eigenvalues are 16 . Using the result in Prob. The discriminant vanishes when , the eigenvalues are . ________________________________________________________________________
page 422 —————————————————————————— CHAPTER 7. ——
. The system of differential equations is The associated eigenvalue problem is
.
The characteristic equation is
, with a single root of
.
Setting
, the algebraic equations reduce to
. An eigenvector is
given by
Hence one solution is
.
A second solution is obtained from a generalized eigenvector whose components satisfy
.
It follows that and A second linearly independent solution is Dropping the last term, the general solution is Imposing the initial conditions, we require that
,
which results in 18 and Therefore the solution of the IVP is . The eigensystem is obtained from analysis of the equation ________________________________________________________________________
page 423 —————...
View
Full Document
 Spring '08
 Staff
 Linear Algebra, eigenvector

Click to edit the document details