Chapter 3.2, Problem 3E

In Exercises $1-10$
(a) compute the eigenvalues;
(b) for each eigenvalue, compute the associated eigenvectors;
(c) using HPGSystemSolver, sketch the direction field for the system, and plot the straight-line solutions;
(d) for each eigenvalue, specify a corresponding straight-line solution and plot its $x(t)$ and $y(t)$ -graphs; and
(e) if the system has two distinct eigenvalues, compute the general solution.
3.
$\left(\begin{array}{l}\frac{dx}{dt}\hfill \\ \frac{dy}{dt}\hfill \end{array}\right)=\left(\begin{array}{ll}-5\hfill & -2\hfill \\ -1\hfill & -4\hfill \end{array}\right)\left(\begin{array}{l}x\hfill \\ y\hfill \end{array}\right)$