Question: Make a change of variable that decouples the equation x' = Ax. Write the equation x (t) = Py (t) and show the calculation that leads to the uncoupled system y' = Dy, specifying P and D.
A as in Exercise
Exercise 5: Solve the initial value problem x' (t) = Ax (t) for t ≥ 0, with x (0) = (3, 2). Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described by x' = Ax. Find the directions of greatest attraction and/or repulsion. When the origin is a saddle point, sketch typical trajectories
