Consider the differential equations dx dt 4x+y+z dy dt = 2x + 5y + 4z dz = -x-y dr Show that if it is assumed that there are solutions of the form x = ae¹¹, y = Bet and z= yet then the system of equations can be transformed into the eigenvalue problem 4 1 α α 2 5 4 BAB 3 11 -10 Y 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 dt 4x+y+z dy dt = 2x + 5y + 4z dz = -x-y dr Show that if it is assumed that there are solutions of the form x = ae¹¹, y = Bet and z= yet then the system of equations can be transformed into the eigenvalue problem 4 1 α α 2 5 4 BAB 3 11 -10 Y Show that the eigenvalues for this problem are 5, 3 and 1, and find the eigenvectors corresponding to the smallest eigenvalue.
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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Question
Clearly written will all steps explained
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8222824-b0b2-4366-bd51-0b90537c8121%2Ffbf7d420-8e21-446e-ab1a-5e4e871a062b%2Frg28m2s_processed.jpeg&w=3840&q=75)
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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