If my matrix contributes eigenvalue A = 3+ 4i with corresponding eigenvector v = [i, 1]. What are the two basis solutions? O 71 = e"[- sin(3t), cos(3t)], a 2 = e"[cos(3t), sin(3t)], O71= e[– sin(4t), cos(4t)], a 2 = e"[cos(4t), sin(4t)], O 71 = e"[- sin(4t), sin(4t)], *2 = e"[cos(4t), cos(4t)],
If my matrix contributes eigenvalue A = 3+ 4i with corresponding eigenvector v = [i, 1]. What are the two basis solutions? O 71 = e"[- sin(3t), cos(3t)], a 2 = e"[cos(3t), sin(3t)], O71= e[– sin(4t), cos(4t)], a 2 = e"[cos(4t), sin(4t)], O 71 = e"[- sin(4t), sin(4t)], *2 = e"[cos(4t), cos(4t)],
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
![If my matrix contributes eigenvalue \( \lambda = 3 + 4i \) with corresponding eigenvector \( \vec{v} = [i, 1] \), what are the two basis solutions?
Options:
1. \( \vec{x}_1 = e^{4t}[-\sin(3t), \cos(3t)], \quad \vec{x}_2 = e^{4t}[\cos(3t), \sin(3t)] \)
2. \( \vec{x}_1 = e^{3t}[-\sin(4t), \cos(4t)], \quad \vec{x}_2 = e^{3t}[\cos(4t), \sin(4t)] \)
3. \( \vec{x}_1 = e^{3t}[-\sin(4t), \sin(4t)], \quad \vec{x}_2 = e^{3t}[\cos(4t), \cos(4t)] \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6cee183-215d-43ed-a508-06b044f7e9eb%2F9add83b7-04ea-419f-b011-211aa98c3c76%2Fwrw771p_processed.png&w=3840&q=75)
Transcribed Image Text:If my matrix contributes eigenvalue \( \lambda = 3 + 4i \) with corresponding eigenvector \( \vec{v} = [i, 1] \), what are the two basis solutions?
Options:
1. \( \vec{x}_1 = e^{4t}[-\sin(3t), \cos(3t)], \quad \vec{x}_2 = e^{4t}[\cos(3t), \sin(3t)] \)
2. \( \vec{x}_1 = e^{3t}[-\sin(4t), \cos(4t)], \quad \vec{x}_2 = e^{3t}[\cos(4t), \sin(4t)] \)
3. \( \vec{x}_1 = e^{3t}[-\sin(4t), \sin(4t)], \quad \vec{x}_2 = e^{3t}[\cos(4t), \cos(4t)] \)
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