In Exercise, perform steps i) and ii) for to the linear systemx' = Ax,where A is the g...

In Exercise, perform steps i) and ii) for to the linear system

x' = Ax,

where A is the given matrix.

i) Find the type type of the equilibrium point at the orign. Do this without the aid of any technology or pplane6. You may, of course, check your answer using pplane.

ii) Use pplane6 to plot several solution curves?enough to fully illustrate the the behavior of the system. You will find it convenient to use the "linear system" choice from the Gallery Menu. If the eigenvalues are real, use the "keyboard input" option to include straight line solutions starting ±10 times the eigenvectors. If the equilibrium point is a saddle point, compute end plate separatrices.