In each of Problems 24 through 27 the eigenvalues and eigenvectors of a matrix A are given.
Consider the corresponding system $x' = Ax$.
(a) Sketch a phase portrait of the system.
(b) Sketch the trajectory passing through the initial point (2,3).
(c) For the trajectory in part (b) sketch the graphs of $x_1$ versus $t$ and of $x_2$ versus $t$ on the same
set of axes.
24. $r_1 = -1$, $\xi^{(1)} = \begin{pmatrix} -1\\2 \end{pmatrix}$; $r_2 = -2$, $\xi^{(2)} = \begin{pmatrix} 1\\2 \end{pmatrix}$
25. $r_1 = 1$, $\xi^{(1)} = \begin{pmatrix} -1\\2 \end{pmatrix}$; $r_2 = -2$, $\xi^{(2)} = \begin{pmatrix} 1\\2 \end{pmatrix}$
26. $r_1 = -1$, $\xi^{(1)} = \begin{pmatrix} -1\\2 \end{pmatrix}$; $r_2 = 2$, $\xi^{(2)} = \begin{pmatrix} 1\\2 \end{pmatrix}$
27. $r_1 = 1$, $\xi^{(1)} = \begin{pmatrix} 1\\2 \end{pmatrix}$; $r_2 = 2$, $\xi^{(2)} = \begin{pmatrix} 1\\-2 \end{pmatrix}$
