-4 = [₁ 1 * *₁ = = [²], (1) then system (1) can also be solved using a diagonalization technique. In this group activities, you and your team members will be guided to employ this approach: } a) By letting A = [ first, each team member should be (fully) convinced that the eigenvalues and its corresponding eigenvectors of A are A₁ = -1 (eigenvector: [2₁]) and A₂ (eigenvector: []). Then, based on this information, propose a matrix P consisting of your = -2 3 eigenvectors. Next, propose a matrix D, which is a diagonal matrix consisting of your eigenvalues. Describe what happens when you perform a matrix multiplication: PDP-1. b) Note that e At = PeDt p-1 (you can see this by generalising the patterns for A², A³, ..., A"). Hence, work out the solution of system (1), x (t).
-4 = [₁ 1 * *₁ = = [²], (1) then system (1) can also be solved using a diagonalization technique. In this group activities, you and your team members will be guided to employ this approach: } a) By letting A = [ first, each team member should be (fully) convinced that the eigenvalues and its corresponding eigenvectors of A are A₁ = -1 (eigenvector: [2₁]) and A₂ (eigenvector: []). Then, based on this information, propose a matrix P consisting of your = -2 3 eigenvectors. Next, propose a matrix D, which is a diagonal matrix consisting of your eigenvalues. Describe what happens when you perform a matrix multiplication: PDP-1. b) Note that e At = PeDt p-1 (you can see this by generalising the patterns for A², A³, ..., A"). Hence, work out the solution of system (1), x (t).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 18EQ
Related questions
Question
![-4
= [₁ 1 *
*₁
=
= [²],
(1)
then system (1) can also be solved using a diagonalization technique. In this group activities, you and
your team members will be guided to employ this approach:
}
a) By letting A = [
first, each team member should be (fully) convinced that the
eigenvalues and its corresponding eigenvectors of A are λ₁ = -1 (eigenvector: [2₁]) and A₂
(eigenvector: []). Then, based on this information, propose a matrix P consisting of your
= -2
3
eigenvectors. Next, propose a matrix D, which is a diagonal matrix consisting of your eigenvalues.
Describe what happens when you perform a matrix multiplication: PDP-1.
b) Note that e At = PeDt p-1 (you can see this by generalising the patterns for A², A³, ..., A"). Hence,
work out the solution of system (1), x (t).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60abd4de-ba2d-4a53-b8fc-e1d2e0799cec%2F0bba1e69-c08e-41fc-9805-0924f2ad8f86%2Fjjn28x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:-4
= [₁ 1 *
*₁
=
= [²],
(1)
then system (1) can also be solved using a diagonalization technique. In this group activities, you and
your team members will be guided to employ this approach:
}
a) By letting A = [
first, each team member should be (fully) convinced that the
eigenvalues and its corresponding eigenvectors of A are λ₁ = -1 (eigenvector: [2₁]) and A₂
(eigenvector: []). Then, based on this information, propose a matrix P consisting of your
= -2
3
eigenvectors. Next, propose a matrix D, which is a diagonal matrix consisting of your eigenvalues.
Describe what happens when you perform a matrix multiplication: PDP-1.
b) Note that e At = PeDt p-1 (you can see this by generalising the patterns for A², A³, ..., A"). Hence,
work out the solution of system (1), x (t).
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