State the Eigenvalue Method for Homogeneous Systems?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.CR: Chapter 10 Review
Problem 62CR
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Question
State the Eigenvalue Method for Homogeneous Systems?
Expert Solution
Step 1
consider a homogenous system
this can be written as
step 1
for calculating the eigenvalue , subtract from the diagonal elements of the matrix
Step 2
find the determinant of the matrix by putting it equal to zero.
simplify the equation and find the roots of it
using the result that if
implies either
Step 3
thus, we get two eigenvalues of the system
step 2
find the eigenvectors corresponding to eigenvalues
put into
that is
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