2. For the matrix-vector DE ' = }}} |x with initial condition ☞ (0) = [−8] a. Find the specific solution using eigenvalues and eigenvectors. b. Sketch the phase portrait. Draw the eigenvector lines and use arrows to note whether they exhibit growth or decay. Then fill in some curved trajectories through the rest of the space. C. The origin x = O is an equilibrium solution. What type (node, saddle, spiral), and what is its stability (unstable, stable, semi-stable)?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter14: Data Mining
Section14.2: Classification Methods
Problem 11P
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2. For the matrix-vector DE ' =
}}}
|x with initial condition ☞ (0) = [−8]
a.
Find the specific solution using eigenvalues and eigenvectors.
b. Sketch the phase portrait. Draw the eigenvector lines and use arrows to note whether they
exhibit growth or decay. Then fill in some curved trajectories through the rest of the space.
C.
The origin x
=
O is an equilibrium solution. What type (node, saddle, spiral), and what is its
stability (unstable, stable, semi-stable)?
Transcribed Image Text:2. For the matrix-vector DE ' = }}} |x with initial condition ☞ (0) = [−8] a. Find the specific solution using eigenvalues and eigenvectors. b. Sketch the phase portrait. Draw the eigenvector lines and use arrows to note whether they exhibit growth or decay. Then fill in some curved trajectories through the rest of the space. C. The origin x = O is an equilibrium solution. What type (node, saddle, spiral), and what is its stability (unstable, stable, semi-stable)?
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