Examine your phase portraits in Problem 51. Under what conditions will the phase portrait of a 2× 2 homogeneous linear system with complex eigenvalues consist of a family of closed curves? Consist of a family of spirals? Under what conditions is the origin (0, 0) a repeller? An attractor? Problem 51 Find phase portraits for the systems in Problems 38-40. Problems 38 Find the general solution of the given system. Problems 40 Find the general solution of the given system.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 15AEXP
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Examine your phase portraits in Problem 51. Under what conditions will the phase portrait of a 2× 2 homogeneous linear system with complex eigenvalues consist of a family of closed curves? Consist of a family of spirals? Under what conditions is the origin (0, 0) a repeller? An attractor?

Problem 51

Find phase portraits for the systems in Problems 38-40.

Problems 38

Find the general solution of the given system.

Problems 40

Find the general solution of the given system.


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