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Fundamental matrices

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(See attached file for full problem description with the matrix)

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a) Write the fundamental matrix for the system:

b) Compute the exponential matrix where A is the matrix in part a).
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Solution Summary

The expert writes the fundamental matrix for the system. The exponential matrix where A is the matrix in part a is determined.

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Please find the attached solution.

a) Write the fundamental matrix for the system:

b) Compute the exponential matrix where A is the matrix in part a).

Solution:

a)
Step1: Eigen-values for the matrix A =

Then the characteristic equation:

- =>

 (1-)(2-)2 = 0
  = 1,  = 2,2 (repeated solutions)

Hence the required eigen-values are ...

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