Categorize the eigenvalues and eigenvectors of the coefficient matrix A according to the accompanying classifications and sketch the phase portrait of the system by hand. Then use a computer system or graphing calculator to check your answer. Click here to view page 1 of Gallery of Typical Phase Portraits for the System x'=Ax: Nodes Click here to view page 2 of Gallery of Typical Phase Portraits for the System x'=Ax: Nodes Click here to view page 3 of Gallery of Typical Phase Portraits for the System x'=Ax: Nodes The system shows a saddle point System of equations Matrix equation '= -2x₁ - 5x2 X₁ x₂ = 4x₁ + 2x2 -2-5 4 Eigenvectors Eigenvalues 21,2 = ± 14 and its eigenvalues are distinct, opposite in sign, and real. x' = V1,2 2 1±i2 -2
Categorize the eigenvalues and eigenvectors of the coefficient matrix A according to the accompanying classifications and sketch the phase portrait of the system by hand. Then use a computer system or graphing calculator to check your answer. Click here to view page 1 of Gallery of Typical Phase Portraits for the System x'=Ax: Nodes Click here to view page 2 of Gallery of Typical Phase Portraits for the System x'=Ax: Nodes Click here to view page 3 of Gallery of Typical Phase Portraits for the System x'=Ax: Nodes The system shows a saddle point System of equations Matrix equation '= -2x₁ - 5x2 X₁ x₂ = 4x₁ + 2x2 -2-5 4 Eigenvectors Eigenvalues 21,2 = ± 14 and its eigenvalues are distinct, opposite in sign, and real. x' = V1,2 2 1±i2 -2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Categorize the eigenvalues and eigenvectors of the coefficient matrix A according to the
accompanying classifications and sketch the phase portrait of the system by hand. Then
use a computer system or graphing calculator to check your answer.
Click here to view page 1 of Gallery of Typical Phase Portraits for the System x'=Ax: Nodes
Click here to view page 2 of Gallery of Typical Phase Portraits for the System x'=Ax: Nodes
Click here to view page 3 of Gallery of Typical Phase Portraits for the System x'=Ax: Nodes
The system shows
a saddle point
System of equations Matrix equation
|x₁' = -2x₁ - 5x₂
x₂ = 4x1 + 2x2
-2 -5
4 2
Eigenvectors
Eigenvalues
21,2= ± 14
and its eigenvalues are distinct, opposite in sign, and real.
x' =
V1,2=
1+ i2
-2
X
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