2. Let (2 2 -2 A = | 5 1 1 5 -3, -3 a. Compute e4 using the definition of the matrix exponential. b. What is the general solution to ' = A? c. Without using the characteristic polynomial of A, what are the eigenvalues of A?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
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2. Let
2 2
A =
1
-3
1
-3
a. Compute eA using the definition of the matrix exponential.
b. What is the general solution to a' = Ax?
c. Without using the characteristic polynomial of A, what are the eigenvalues of A?
Transcribed Image Text:2. Let 2 2 A = 1 -3 1 -3 a. Compute eA using the definition of the matrix exponential. b. What is the general solution to a' = Ax? c. Without using the characteristic polynomial of A, what are the eigenvalues of A?
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