Explanation Given: The given matrix is, A = [ − 4 0 0 − 4 ] Approach: The equilibrium condition corresponding to the eigenvalues are shown in table below, Eigenvalues Equilibrium Real and negative Stable node Real and positive Unstable node Opposite signs Saddle Complex with negative real part Stable spiral Complex with positive real part Unstable spiral Calculation: Consider the given matrix, A = [ − 4 0 0 − 4 ] The eigenvalue of the above matrix are λ 1 = − 4 , and λ 2 = − 4

Differential Equations and Linear Algebra (4th Edition)

4th Edition

ISBN: 9780321964670

Author: Stephen W. Goode, Scott A. Annin

Publisher: PEARSON

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Chapter 9.11, Problem 37AP

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The characterization of the equilibrium point for the system x′=Ax and sketch the phase portrait.

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Chapter 9.11, Problem 36AP

Chapter 9.11, Problem 38AP

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Chapter 9 Solutions

Differential Equations and Linear Algebra (4th Edition)

Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - Prob. 5TFR Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - Prob. 7TFR Ch. 9.1 - For Question a-j, decide if the given statement is...Ch. 9.1 - Prob. 9TFR Ch. 9.1 - Prob. 10TFR

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The characterization of the equilibrium point for the system x ′ = A x and sketch the phase portrait.

Solution Summary: The author explains that the equilibrium point is a stable node. The eigenvalues are real and negative.

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To find:

The characterization of the equilibrium point for the system x′=Ax and sketch the phase portrait.

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Chapter 9 Solutions

The characterization of the equilibrium point for the system x ′ = A x and sketch the phase portrait.

Solution Summary: The author explains that the equilibrium point is a stable node. The eigenvalues are real and negative.

Concept explainers

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To find: The characterization of the equilibrium point for the system x′=Ax and sketch the phase portrait.

Want to see the full answer?

Chapter 9 Solutions

To find:

The characterization of the equilibrium point for the system x′=Ax and sketch the phase portrait.