For each system in 7-12, find the eigenpairs (you will probably want to use technology
for this) and sketch by hand a phase portrait for the system. If the eigenvalues are
real, the eigenvectors should be included in the sketch. Put arrows on each solution
trajectory to denote the direction of motion.
Solve for 8, 10, and 12. Please show sketches.
7. x' = x + 2y, y' = -2x - 2y
8. x' = 2x + 3y, y' = -x
9. x' = -4x + 2y, y' = -x + y
10. x' = -x + y, y' = x - 2y
11. x' = 2x + 3y, y' = -2x - 2y
12. x' = x + 2y, y' = x + 3y
