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(Solved): 4. Consider the non-homogeneous linear system x = 5 1 3 1 x + 2e 2t ...
![4. Consider the non-homogeneous linear system
\[
\dot{\mathbf{x}}=\left[\begin{array}{cc}
5 & -1 \\
3 & 1
\end{array}\right]](https://media.cheggcdn.com/media/5f8/5f80d99c-e069-474e-9e60-07638c464827/phpV0YFDM)
4. Consider the non-homogeneous linear system (a) Determine a fundamental matrix for the associated homogeneous system. (b) Determine the inverse of the fundamental matrix. (c) Find a particular solution. (d) Find the general solution of the system.
Expert Answer
Solution: The non-homogeneous system is, (1)Here, The eigen values are given by (a) Let the eigen vector corresponding to be Let the eigen vector corresponding to be