Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. (-3+i) A₁ = 1 71 = y == b. Find the real-valued solution to the initial value problem [{ {9/2 (5-5/2)e^(-it)+(5+5/2)^(it) Use t as the independent variable in your answers. vi(t) =(5-5/2i)e^(-it)(-3/5-1/5)+(5+5/2i)e^(it)(-3/5+i/5) 32 (1) and A₂ = -3y1 - 232, 591 +39/2, 4 V₂ = 3/1 (0) = 6, 3/2 (0) = -5. (-3-1)/ 1
Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. (-3+i) A₁ = 1 71 = y == b. Find the real-valued solution to the initial value problem [{ {9/2 (5-5/2)e^(-it)+(5+5/2)^(it) Use t as the independent variable in your answers. vi(t) =(5-5/2i)e^(-it)(-3/5-1/5)+(5+5/2i)e^(it)(-3/5+i/5) 32 (1) and A₂ = -3y1 - 232, 591 +39/2, 4 V₂ = 3/1 (0) = 6, 3/2 (0) = -5. (-3-1)/ 1
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
![Consider the linear system
a. Find the eigenvalues and eigenvectors for the coefficient matrix.
(-3+i)
A₁ = 1
, vi
b. Find the real-valued solution to the initial value problem
[{
and A₂ =
-3y1 - 2/2,
591 +33/2,
Use t as the independent variable in your answers.
vi(t) =(5-5/2i)e^(-it)(-3/5-1/5)+(5+5/2i)e^(it)(-3/5+i/5)
32(t)= (5-5/2)^(-it)+(5+5/2)^(it)
4
vo =
3/1 (0) = 6,
3/2 (0) = -5.
(-3-1)/](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc84ba02-cd45-4ad4-9c89-9c840cb88804%2F1328d1f7-a9ea-4c55-8198-e486f469cffa%2Fpz7lk8h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the linear system
a. Find the eigenvalues and eigenvectors for the coefficient matrix.
(-3+i)
A₁ = 1
, vi
b. Find the real-valued solution to the initial value problem
[{
and A₂ =
-3y1 - 2/2,
591 +33/2,
Use t as the independent variable in your answers.
vi(t) =(5-5/2i)e^(-it)(-3/5-1/5)+(5+5/2i)e^(it)(-3/5+i/5)
32(t)= (5-5/2)^(-it)+(5+5/2)^(it)
4
vo =
3/1 (0) = 6,
3/2 (0) = -5.
(-3-1)/
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