4. Use A = (3-2) for the following questions. (a) Find a fundamental matrix for the system of equations x' = Ax. (b) Find the fundamental matrix Þ(t) for the system x' = Ax which satisfies (0) = I. (²) (c) Use (t) to find the solution which has initial value x(0) =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Row reduction

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Finding eigenvalues and eigenvectors

4. Use A
=
2
(3²
-1
-2
for the following questions.
(a) Find a fundamental matrix for the system of equations a' = Ax.
(b) Find the fundamental matrix Þ(t) for the system x' = Ax which satisfies Þ(0) = I.
- (²)
(c) Use Þ(t) to find the solution which has initial value x(0)
=
Transcribed Image Text:4. Use A = 2 (3² -1 -2 for the following questions. (a) Find a fundamental matrix for the system of equations a' = Ax. (b) Find the fundamental matrix Þ(t) for the system x' = Ax which satisfies Þ(0) = I. - (²) (c) Use Þ(t) to find the solution which has initial value x(0) =
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