Problem $1$: Consider the system of differential equations

$,$ with initial conditions

and $.$

a$)$ Compute the eigenvalues and eigenvectors of the system.

Solution:

$[$Insert your math$/$explanation here.$]$

b$)$ Compute the solution to the system of differential equations.

Solution:

$[$Insert your math$/$explanation here.$]$

c$)$ Use MATLAB to plot the direction field and eigenvectors of the system.

Solution:

$\%[$Insert your MATLAB code and plot here.$]$

d$)$ Use MATLAB to plot the phase portrait of the system.

Solution:

$\%[$Insert your MATLAB code and plot here.$]$

d$)$ Use your phase portrait or numerical analysis to identify and classify any critical