Problem 5. Consider the one-parameter family of linear systems depending on the parameter a. This family determines a curve in the trace-determinant plane (a) sketch the corresponding curve in the trace-determinant plane; (b) in a brief essay, discuss different types of behaviors exhibited by the system as a increases along the real line (unless otherwise noted); and I (c) identify the values of a where the type of the system changes. These are the bifurcation values of a. dY dt = (2) Y,