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(₁ 4 (a) Find the general solution of the system of equations x' = Ax. 1. Use A = -4 for the following questions.

(₁ 4 (a) Find the general solution of the system of equations x' = Ax. 1. Use A = -4 for the following questions.

Advanced Engineering Mathematics
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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You may use a calculator to perform basic calculations on these problems: ? Row reduction

? Matrix multiplication

? Matrix inverses

? Finding eigenvalues and eigenvectors

This will greatly reduce the amount of time you have to spend on the assignment. I only ask that you show what steps you are taking.

Please show your process for calculating generalized eigenvectors.

1. Use A = (13) 4 for the following questions. (a) Find the general solution of the system of equations x' = Ax. (b) Find the fundamental matrix Þ(t) for the system x' = Ax which satisfies (0) = I. (c) Use Þ(t) to find the solution which has initial value x(0) = (2). (d) Find a Jordan Form J for the matrix A.
Transcribed Image Text:1. Use A = (13) 4 for the following questions. (a) Find the general solution of the system of equations x' = Ax. (b) Find the fundamental matrix Þ(t) for the system x' = Ax which satisfies (0) = I. (c) Use Þ(t) to find the solution which has initial value x(0) = (2). (d) Find a Jordan Form J for the matrix A.
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