Alpha and omega limit sets

Question

What are all the possible $α$- and $ω$-limit sets of points for the linear system of equations $x'=Ax$ given by the following matrices $A$:

I guess I don't really know how to get started, Could I have some guidance? So I was told to calculate the eigenvalues (fine) and eigenvectors (I kind of forgot how to do that...)

1. $ A= \left[ {\begin{array}{cc} -4 & -2 \\ 3 & 11 \\ \end{array} } \right] $

$λ_1=-10$ $λ_2=-5$

for $λ_1=-10$:

eigenvector $ = \left[ {\begin{array}{cc} 1 \\ 3 \\ \end{array} } \right] $

for $λ_2=-5$:

eigenvector $ = \left[ {\begin{array}{cc} 2 \\ 1 \\ \end{array} } \right] $

2. $ A= \left[ {\begin{array}{cc} 1 & 1 \\ 3 & 1 \\ \end{array} } \right] $

$λ_1=4$ $λ_2=-2$

for $λ_1=4$:

eigenvector $ = \left[ {\begin{array}{cc} 1 \\ 1 \\ \end{array} } \right] $

for $λ_2=-2$:

eigenvector $ = \left[ {\begin{array}{cc} -1 \\ 1 \\ \end{array} } \right] $

3. $ A= \left[ {\begin{array}{cc} 4 & 5 \\ -5 & -2 \\ \end{array} } \right] $

$λ_1=1+4i$ $λ_2=1-4i$

for $λ_1=1+4i$:

eigenvector $ = \left[ {\begin{array}{cc} -3/5-(4i)/5 \\ 1 \\ \end{array} } \right] $

for $λ_1=1-4i$:

eigenvector $ = \left[ {\begin{array}{cc} -3/5+(4i)/5 \\ 1 \\ \end{array} } \right]$