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For the following systems, the origin is the equilibrium point. 3. a) Write each system in matrix form 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. dx dt 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. dx dt dy dt = Ax. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) = 4x - 13y = 2x - 6y

For the following systems, the origin is the equilibrium point. 3. a) Write each system in matrix form 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. dx dt 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. dx dt dy dt = Ax. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) = 4x - 13y = 2x - 6y

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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For the following systems, the origin is the equilibrium point. 3. a) Write each system in matrix form 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. dx dt 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. dx dt dy dt = Ax. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) = 4x - 13y = 2x - 6y
Transcribed Image Text:For the following systems, the origin is the equilibrium point. 3. a) Write each system in matrix form 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. dx dt 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. dx dt dy dt = Ax. f) If A has real eigenvalues, then determine the eigenvectors and use diagonalization to solve the system. (See examples in Section 7.4) = 4x - 13y = 2x - 6y
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