Discuss the geometric nature of the solutions to the linear system X AX given the
Chapter 11, Problem 12(choose chapter or problem)
Discuss the geometric nature of the solutions to the linear system \(\mathbf{X}^{\prime}=\mathbf{A X}\) given the general solution.
(a) \(\mathbf{X}(t)=c_{1}\left(\begin{array}{l}1 \\ 1\end{array}\right) e^{-t}+c_{2}\left(\begin{array}{r}1 \\ -2\end{array}\right) e^{-2 t}\)
(b) \(\mathbf{X}(t)=c_{1}\left(\begin{array}{r}1 \\ -1\end{array}\right) e^{-t}+c_{2}\left(\begin{array}{l}1 \\ 2\end{array}\right) e^{2 t}\)
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