Consider the following system. dx dt Find the eigenvalues and eigenvectors. Number of eigenvectors: Two r1 -1 12 2 §(¹) "- (3³) = 5 - (₁ -¹8 ) x 1 = (²) - ( 8 ) Classify the critical point (0,0) as to type and determine whether it is stable, asymptotically stable, or unstable. The critical point (0,0) is Choose one

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 65E
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Choose one
a saddle point
an unstable node
an asymptotically stable node
an unstable spiral
an asymptotically stable spiral
Transcribed Image Text:Choose one a saddle point an unstable node an asymptotically stable node an unstable spiral an asymptotically stable spiral
Consider the following system.
dx
dt
Find the eigenvalues and eigenvectors.
Number of eigenvectors: Two
r1
-1
§(¹)
=
12 2
(3³)
(²) - ( 8 )
Classify the critical point (0,0) as to type and determine whether it
is stable, asymptotically stable, or unstable.
The critical point (0,0) is Choose one
5
- (₁ -¹8 ) x
1
=
Transcribed Image Text:Consider the following system. dx dt Find the eigenvalues and eigenvectors. Number of eigenvectors: Two r1 -1 §(¹) = 12 2 (3³) (²) - ( 8 ) Classify the critical point (0,0) as to type and determine whether it is stable, asymptotically stable, or unstable. The critical point (0,0) is Choose one 5 - (₁ -¹8 ) x 1 =
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