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For each of the following linear systems (a) Find the eigenvalues and their corresponding eigenvectors (b) Analyse the stability and determine the nature of the critical point (0, 0). (c) Sketch several trajectories in the phase plane dx 1. dt 2 - (: 1)- (): dx dx 3. dt 3 dt 3 -2 dx 4. dt dx 5. dt 1-5 2 -5 -3 6. dt -2

For each of the following linear systems (a) Find the eigenvalues and their corresponding eigenvectors (b) Analyse the stability and determine the nature of the critical point (0, 0). (c) Sketch several trajectories in the phase plane dx 1. dt 2 - (: 1)- (): dx dx 3. dt 3 dt 3 -2 dx 4. dt dx 5. dt 1-5 2 -5 -3 6. dt -2

Elementary Linear Algebra (MindTap Course List)
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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For each of the following linear systems (a) Find the eigenvalues and their corresponding eigenvectors (b) Analyse the stability and determine the nature of the critical point (0, 0). (c) Sketch several trajectories in the phase plane dx 1. dt 2 -( )- (): dx dx 3. dt 3 2 dt 3 dx 4. dt #- ()* dx 5. dt -5 2 -5 -3 6. dt
Transcribed Image Text:For each of the following linear systems (a) Find the eigenvalues and their corresponding eigenvectors (b) Analyse the stability and determine the nature of the critical point (0, 0). (c) Sketch several trajectories in the phase plane dx 1. dt 2 -( )- (): dx dx 3. dt 3 2 dt 3 dx 4. dt #- ()* dx 5. dt -5 2 -5 -3 6. dt
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