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Exercise:
The figure shows the phase portrait for a two-dimensional system of linear differential s. center includegraphicswidthcm#image_path:phasportrait-# center Which of the following statements can be true? Give reasons for your answers also why a statement cannot be true. abcliste abc The eigenvalues are and . abc The eigenvalues are - and -. abc The eigenvalues are i and -i. abc The eigenvectors are vec v_ pmatrix pmatrix quad textrmand quad vec v_ pmatrix pmatrix abc The eigenvectors are vec v_ pmatrix - pmatrix quad textrmand quad vec v_ pmatrix pmatrix abcliste

Solution:
The fixed po at the origin is clearly stable so only b can be correct. a would be an unstable fixed po and c a centre. vspacemm The eigenvectors correspond to the straight line solutions. It is clear that they are in different quadrants see figure below so e can be true while d must be wrong. center includegraphicswidthcm#image_path:phasportrait-with-eigenvectors-# center
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Exercise:
The figure shows the phase portrait for a two-dimensional system of linear differential s. center includegraphicswidthcm#image_path:phasportrait-# center Which of the following statements can be true? Give reasons for your answers also why a statement cannot be true. abcliste abc The eigenvalues are and . abc The eigenvalues are - and -. abc The eigenvalues are i and -i. abc The eigenvectors are vec v_ pmatrix pmatrix quad textrmand quad vec v_ pmatrix pmatrix abc The eigenvectors are vec v_ pmatrix - pmatrix quad textrmand quad vec v_ pmatrix pmatrix abcliste

Solution:
The fixed po at the origin is clearly stable so only b can be correct. a would be an unstable fixed po and c a centre. vspacemm The eigenvectors correspond to the straight line solutions. It is clear that they are in different quadrants see figure below so e can be true while d must be wrong. center includegraphicswidthcm#image_path:phasportrait-with-eigenvectors-# center
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Attributes & Decorations
Branches
Differential equations
Tags
eigenvalue, eigenvector, phase portrait
Content image
Difficulty
(2, default)
Points
3 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration