(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.

dx = -x 2y dt dy =x - 4y dt