9.1.1

eigenvectordirection=Plot[{2x1,1/2x1},{x1,-2,2},PlotStyle->{{Thick,Red},{Thick,Red}}];

field=VectorPlot[{3x1-2x2,2x1-2x2},{x1,-2,2},{x2,-2,2},VectorScale->{Tiny,1},VectorPoints->20];

Show[field,eigenvectordirection]

9.1.3

eigenvectordirection=Plot[{x1,3x1},{x1,-2,2},PlotStyle->{{Thick,Red},{Thick,Red}}];

field=VectorPlot[{2x1-x2,3x1-2x2},{x1,-2,2},{x2,-2,2},VectorScale->{Tiny,1},VectorPoints->20];

Show[field,eigenvectordirection]

9.1.10

It's difficult to get the eigenvalue "direction" by hand here, since the trajectories are ellipses. We'll just rely on the vector field to verify.

field=VectorPlot[{1x1+2x2,-5x1-x2},{x1,-1,1},{x2,-1,1},VectorScale->{Tiny,1},VectorPoints->20]