the equations of the straight-line trajectories and tell whether they are going ds or away from the origin. If none exist, state so. as real eigenvalues, then determine the eigenvectors and use diagonalization to the system. (See examples in Section 7.4) x + 2y x + 5y (Ctrl) -

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.
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.
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)
2.
dx
dt
dy
dt
= 5x + 2y
= 2x + 5y
(Ctrl)
dx
dt
= Ax.
Transcribed Image Text:For the following systems, the origin is the equilibrium point. 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. 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) 2. dx dt dy dt = 5x + 2y = 2x + 5y (Ctrl) dx dt = Ax.
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