2. (a) Let A be a square matrix of order tv 11 with the corresponding and V = Find exponential solutions (t) = = equations x'' = AX.
2. (a) Let A be a square matrix of order tv 11 with the corresponding and V = Find exponential solutions (t) = = equations x'' = AX.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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![2
2. (a) Let A be a square matrix of order two which has eigenvectors u =
園
exponential solutions X(t) = [52]
ALL
[x₁(t)]
[₂(t)]
and =
Find
with the corresponding eigenvalues λ = 2 and λ = -5.
of the system of differential
equations x'' = AX.
(b) How do x₁ (t) and x2 (t)| behave in the found solutions as t→ ∞o?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F801d34df-dcab-45aa-85e0-2349cce424a4%2F7e7f4b97-6bca-4930-b683-542c1e122bc6%2Fec51im8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2
2. (a) Let A be a square matrix of order two which has eigenvectors u =
園
exponential solutions X(t) = [52]
ALL
[x₁(t)]
[₂(t)]
and =
Find
with the corresponding eigenvalues λ = 2 and λ = -5.
of the system of differential
equations x'' = AX.
(b) How do x₁ (t) and x2 (t)| behave in the found solutions as t→ ∞o?
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