Practice problem 21.6 You have been given the following second order linear system and its corresponding eigenvalues: A₂ = 36 20 -16] -16 20 A₁ = 4 Guess a solution that has the form of: x = vewt And then substitute it in to (0) = z = Az Then guess what the values of v and w should be in relation to the eigenvectors and eigenvalues of matrix A. you must collect four linearly dependent solutions that are different. Note that a positive numbers square root should have both a - and + answer. Then determine the solution of the initial value problem where: [0] (0) = [8] z₁(t) €* = 2₂(t)=
Practice problem 21.6 You have been given the following second order linear system and its corresponding eigenvalues: A₂ = 36 20 -16] -16 20 A₁ = 4 Guess a solution that has the form of: x = vewt And then substitute it in to (0) = z = Az Then guess what the values of v and w should be in relation to the eigenvectors and eigenvalues of matrix A. you must collect four linearly dependent solutions that are different. Note that a positive numbers square root should have both a - and + answer. Then determine the solution of the initial value problem where: [0] (0) = [8] z₁(t) €* = 2₂(t)=
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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![Practice problem 21.6
You have been given the following second order linear system and its corresponding
eigenvalues:
20 -16]
A₁ = 4
-16 20
Guess a solution that has the form of:
* = vewt
And then substitute it in to
z = Az
Then guess what the values of v and w should be in relation to the eigenvectors and
eigenvalues of matrix A. you must collect four linearly dependent solutions that are different.
Note that a positive numbers square root should have both a - and + answer. Then determine the
solution of the initial value problem where:
[0
0
a'
¹ (0) = [8]
(0) =
z
A₂ = 36
₁ (t)=
#₂(t)=
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd61aa0cc-194b-4783-aa03-3c5c9cda5609%2Fb5506d1c-cbe8-4073-9909-d7d5012848e0%2F1y6v6q5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Practice problem 21.6
You have been given the following second order linear system and its corresponding
eigenvalues:
20 -16]
A₁ = 4
-16 20
Guess a solution that has the form of:
* = vewt
And then substitute it in to
z = Az
Then guess what the values of v and w should be in relation to the eigenvectors and
eigenvalues of matrix A. you must collect four linearly dependent solutions that are different.
Note that a positive numbers square root should have both a - and + answer. Then determine the
solution of the initial value problem where:
[0
0
a'
¹ (0) = [8]
(0) =
z
A₂ = 36
₁ (t)=
#₂(t)=
=
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