Classify the fixed point at the origin and sketch an accurate phase portrait for the following system: $\left\{\begin{matrix} \dfrac{dx}{dt}=36x-16y\\ \dfrac{dy}{dx}=-3x+28y \end{matrix}\right.$
Am I correct in thinking that I need to write these two equations in matrix form, find the eigenvalues and depending on what they are will determine what fixed point I have? To sketch the phase portrait do I then need to know the eigenvectors and directions?