##### Exercise1

For each of the $$2\times2$$ matrices below, determine which of the six types the dynamical system $$\xvec_{k+1}=A\xvec_k$$ belongs to and describe the behavior of typical trajectories as $$k$$ becomes large.

1. $$A = \left[\begin{array}{rr} 3\amp 1 \\ 1 \amp 3 \\ \end{array}\right]\text{.}$$

2. $$A = \left[\begin{array}{rr} 3\amp 2 \\ -1 \amp 2 \\ \end{array}\right]\text{.}$$

3. $$A = \left[\begin{array}{rr} 1.3 \amp 0.3 \\ 0.1 \amp 0.5 \\ \end{array}\right]\text{.}$$

4. $$A = \left[\begin{array}{rr} -2.3\amp -1 \\ 2.5 \amp -0.7 \\ \end{array}\right]\text{.}$$

in-context