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Linear Algebra With Applications
Found in: Page 440
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

For the linear system dxdt=[-2031]x(t)find the matching phase portrait.

The phase portrait corresponds to V

See the step by step solution

Step by Step Solution

Step 1: To find the eigenvalues

Consider the linear system as follows.


To find the eigenvalues, evaluate A-λI=0as follows.


Simplify further as follows.


Simplify further as follows.


Therefore, the eigenvalues are λ1=-2 and λ2=1

Step 2: Observation of the phase portrait

The eigenvalues are λ1=-2 and λ2=1

Since, the eigenvalues are real and distinct are of opposite sign.

Therefore, the phase portrait is in figure 5 as follows.

Hence, the phase portrait to the linear system dxdt=-2031xt is V.

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