Consider the initial value problem (a) Find the eigenvalues and eigenvectors for the coefficient matrix. X₁ x(t) = -3i ₁ (b) Solve the initial value problem. Give your solution in real form. 181 dx dt = 1 -1+i -3 3]x, , and X₂ x(0) = [] 31, ₂ = 1 -1-i
Consider the initial value problem (a) Find the eigenvalues and eigenvectors for the coefficient matrix. X₁ x(t) = -3i ₁ (b) Solve the initial value problem. Give your solution in real form. 181 dx dt = 1 -1+i -3 3]x, , and X₂ x(0) = [] 31, ₂ = 1 -1-i
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 initial value problem
(a) Find the eigenvalues and eigenvectors for the coefficient matrix.
A₁ =
x(t) =
-3i, v₁ =
(b) Solve the initial value problem. Give your solution in real form.
181
#-[31]
=
6
dx
dt.
1
-1+i
X,
x(0) =
and X₂ = 31, 2 =
1
-1-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f523637-2688-4999-8995-e2f7c47c64ad%2Fa429e735-38fe-446e-b1be-7bf29da8ee57%2Fnni0o7v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the initial value problem
(a) Find the eigenvalues and eigenvectors for the coefficient matrix.
A₁ =
x(t) =
-3i, v₁ =
(b) Solve the initial value problem. Give your solution in real form.
181
#-[31]
=
6
dx
dt.
1
-1+i
X,
x(0) =
and X₂ = 31, 2 =
1
-1-
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