Suppose that the matrix A has the following eigenvalues and eigenvectors: D X₁ : -3 + 4i with 7₁ = and 1₂ = -3- 4i with ₂ = [1] Write the general real solution for the linear system 7' = Ar, in the following forms: A. In eigenvalue/eigenvector form: [*] [] = C1 B. In fundamental matrix form: y(t) = + C₂ = + C. As two equations: (write "c1" and "c2" for C₁ and c₂) x(t) = ). e t t
Suppose that the matrix A has the following eigenvalues and eigenvectors: D X₁ : -3 + 4i with 7₁ = and 1₂ = -3- 4i with ₂ = [1] Write the general real solution for the linear system 7' = Ar, in the following forms: A. In eigenvalue/eigenvector form: [*] [] = C1 B. In fundamental matrix form: y(t) = + C₂ = + C. As two equations: (write "c1" and "c2" for C₁ and c₂) x(t) = ). e t t
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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![Suppose that the matrix A has the following eigenvalues and eigenvectors:
D
X₁ : -3 + 4i with 7₁ =
and
1₂ = -3- 4i with ₂ =
[1]
Write the general real solution for the linear system 7' = Ar, in the following forms:
A. In eigenvalue/eigenvector form:
[*]
[]
= C1
B. In fundamental matrix form:
y(t) =
+ C₂
=
+
C. As two equations: (write "c1" and "c2" for C₁ and c₂)
x(t) =
).
e
t
t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05295cc1-71f0-4e3b-b6f8-2c1731c6d617%2F76034fb2-3180-477b-9f8e-6526a93fc02c%2Fuxyvp_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that the matrix A has the following eigenvalues and eigenvectors:
D
X₁ : -3 + 4i with 7₁ =
and
1₂ = -3- 4i with ₂ =
[1]
Write the general real solution for the linear system 7' = Ar, in the following forms:
A. In eigenvalue/eigenvector form:
[*]
[]
= C1
B. In fundamental matrix form:
y(t) =
+ C₂
=
+
C. As two equations: (write "c1" and "c2" for C₁ and c₂)
x(t) =
).
e
t
t
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