Consider the differential equations dx dr = 4x+y+z 2x + 5y + 4z dr dz = -x-y dr Show that if it is assumed that there are solutions of the form x = ae¹, y = Bed and z= ye¹ then the system of equations can be transformed into the eigenvalue problem 4 1 2 54 38-4 B = B -1 -1 Show that the eigenvalues for this problem are 5, 3 and 1, and find the eigenvectors corresponding to the smallest eigenvalue.
Consider the differential equations dx dr = 4x+y+z 2x + 5y + 4z dr dz = -x-y dr Show that if it is assumed that there are solutions of the form x = ae¹, y = Bed and z= ye¹ then the system of equations can be transformed into the eigenvalue problem 4 1 2 54 38-4 B = B -1 -1 Show that the eigenvalues for this problem are 5, 3 and 1, and find the eigenvectors corresponding to the smallest eigenvalue.
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 30E
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Transcribed Image Text:Consider the differential equations
d.x
dt
= 4x+y+z
dy = 2x + 5y + 4z
= -x-y
Show that if it is assumed that there are solutions
of the form x = ae¹, y = ße^ and z = ye¹ then
the system of equations can be transformed into
the eigenvalue problem
4
1
α
α
2 5 4 BAB
32
-1 -1
Show that the eigenvalues for this problem
are 5, 3 and 1, and find the eigenvectors
corresponding to the smallest eigenvalue.
ele ele ele
dz
dt
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