1.) The direction field along with some trajectories in the $x_2$ vs $x_1$ plane for the system of differential equations $x' = Ax$ is drawn below. What can you say about the
eigenvalues of $A$.
a.) $A$ has 2 real positive eigenvalues
b.) $A$ has 2 real negative eigenvalues
c.) $A$ has 1 positive and 1 negative eigenvalue
d.) $A$ has 2 complex eigenvalues, $a \pm bi$ where $a > 0$
e.) $A$ has 2 imaginary eigenvalues, $\pm bi$
f.) $A$ has 2 complex eigenvalues, $a \pm bi$ where $a < 0$
2.) The direction field along with some trajectories in the $x_2$ vs $x_1$ plane for the system of differential equations $x' = Ax$ is drawn below. What can you say about the
eigenvalues of $A$.
a.) $A$ has 2 real positive eigenvalues
b.) $A$ has 2 real negative eigenvalues
c.) $A$ has 1 positive and 1 negative eigenvalue
d.) $A$ has 2 complex eigenvalues, $a \pm bi$ where $a > 0$
e.) $A$ has 2 imaginary eigenvalues, $\pm bi$
f.) $A$ has 2 complex eigenvalues, $a \pm bi$ where $a < 0$
3.) The direction field along with some trajectories in the $x_2$ vs $x_1$ plane for the system of differential equations $x' = Ax$ is drawn below. What can you say about the
eigenvalues of $A$.
a.) $A$ has 2 real positive eigenvalues
b.) $A$ has 2 real negative eigenvalues
c.) $A$ has 1 positive and 1 negative eigenvalue
d.) $A$ has 2 complex eigenvalues, $a \pm bi$ where $a > 0$
e.) $A$ has 2 imaginary eigenvalues, $\pm bi$
f.) $A$ has 2 complex eigenvalues, $a \pm bi$ where $a < 0$
