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For the following systems, the origin is the equilibrium point. dž a) Write each system in matrix form = Determine the eigenvalues of A. dt b) c) State whether the origin is a stable or unstable equilibrium. d) State whether the origin is a node, saddle point, spiral point, or center. e) State the equations of the straight-line trajectories and tell whether they are going towards or away from the origin. If none exist, state so. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) 5. dx dt dy dt = -3x + 4y = 2x - 5y Ax.

For the following systems, the origin is the equilibrium point. dž a) Write each system in matrix form = Determine the eigenvalues of A. dt b) c) State whether the origin is a stable or unstable equilibrium. d) State whether the origin is a node, saddle point, spiral point, or center. e) State the equations of the straight-line trajectories and tell whether they are going towards or away from the origin. If none exist, state so. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) 5. dx dt dy dt = -3x + 4y = 2x - 5y Ax.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 23EQ
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For the following systems, the origin is the equilibrium point. dx a) Write each system in matrix form = Ax. dt 5. b) Determine the eigenvalues of A. c) State whether the origin is a stable or unstable equilibrium. d) State whether the origin is a node, saddle point, spiral point, or center. e) State the equations of the straight-line trajectories and tell whether they are going towards or away from the origin. If none exist, state so. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) dx dt dy dt = -3x + 4y = 2x - 5y
Transcribed Image Text:For the following systems, the origin is the equilibrium point. dx a) Write each system in matrix form = Ax. dt 5. b) Determine the eigenvalues of A. c) State whether the origin is a stable or unstable equilibrium. d) State whether the origin is a node, saddle point, spiral point, or center. e) State the equations of the straight-line trajectories and tell whether they are going towards or away from the origin. If none exist, state so. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) dx dt dy dt = -3x + 4y = 2x - 5y
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