The matrix of a linear dynamic system is: [0, 3] [3, 0]
FACT: If A is the evolution curve that passes on point (1,1) in phase space and B the evolution curve that passes on point (1,-1) we can say that origin is the negative limit of A and positive limit of B.
PROBLEM: My question is how can I see this? In similar questions I use plotdf (on maxima) to see the system but they give me 2 equations of the system not the matrix, per example x'=-y-x^2, y'=x-x^3. But with the matrix I can't see where to begin to solve the problem.
EDIT:
(maxima plotdf graphs)
Point A (1,1):
Point B(1,-1):
And now just for looking at the graph what can we say to get to the fact?
The system $x'=3y$, $y'=3x$ is solvable. If $x(0)=y(0)=1$ then $x(t)=y(t)=\mathrm e^{3t}$ for every $t$ hence $(x(t),y(t))\to(0,0)$ when $t\to-\infty$. If $x(0)=-y(0)=1$ then $x(t)=-y(t)=\mathrm e^{-3t}$ for every $t$ hence $(x(t),y(t))\to(0,0)$ when $t\to+\infty$.
For other initial conditions, it may help to note that $x^2-y^2$ is constant along every solution.