1. Find the eigenvalues of A and the corresponding eigenvectors. 2. Use the results in 1. above to find the general solution of the system and the particular solution satisfying x (0) = [4]. 3. Analyse the stability and determine the nature of the critical point (0,0).
1. Find the eigenvalues of A and the corresponding eigenvectors. 2. Use the results in 1. above to find the general solution of the system and the particular solution satisfying x (0) = [4]. 3. Analyse the stability and determine the nature of the critical point (0,0).
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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![Consider the linear system X'= AX where A is the matrix A = [
1 3
31
1. Find the eigenvalues of A and the corresponding eigenvectors.
2. Use the results in 1. above to find the general solution of the system and the particular solution satisfying
X (0) = [4].
3. Analyse the stability and determine the nature of the critical point (0,0).
4. Sketch several trajectories of the system in the phase plane.
5. Confirm the results in 2. using the exponential of the matrix A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d23c93b-870e-4ad1-8eae-60e3d2381ea8%2Febb68018-0baf-49c5-abdc-2e2d47052f4d%2Fsmypwad_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the linear system X'= AX where A is the matrix A = [
1 3
31
1. Find the eigenvalues of A and the corresponding eigenvectors.
2. Use the results in 1. above to find the general solution of the system and the particular solution satisfying
X (0) = [4].
3. Analyse the stability and determine the nature of the critical point (0,0).
4. Sketch several trajectories of the system in the phase plane.
5. Confirm the results in 2. using the exponential of the matrix A.
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