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
Related questions
Question
Solve all and include all the steps
![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%2Fca63ac5b-84c7-451f-8b25-0f938d4d1bc6%2Fyy00rf7_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
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Similar questions
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage