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For a nonzero solution, we must have
, which is an eigenvalue of multiplicity two. Setting
coefficient matrix reduces the system to the single equation
corresponding eigenvector is
One solution is
x . The only root
. Hence the . In order to obtain a second linearly independent solution, we find a solution of the system
There equations reduce to
. A second solution is . Set , some arbitrary constant. Then x Dropping the last term, the general solution is
page 415 —————————————————————————— CHAPTER 7. ——
6. The eigensystem is obtained from analysis of the equation
The characteristic equation of the coefficient matrix is
, we have , with .
This system is reduced to the equations A corresponding eigenvector vector is given by
the system of equations is reduced to the single equation Setting , An eigenvector vector is given by
Since the last equation has two
free variables, a third linearly independent eigenvector associated with
Therefore the general s...
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This note was uploaded on 03/11/2014 for the course MA 303 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.
- Spring '08