To run the whole notebook, select all, and then type “shift enter”.  
Alternatively, click in a “cell” (you will see the blinking cursor in the cell) and then type “shift enter”.  This runs just this one cell.

The figures are not seen until you run the cells.  This makes the notebook much smaller.

size = 720; (* make a multiple of 3*)
SetDirectory["/Users/james/Dropbox/classes/MAT 239 2020.1/evecFigs" ] (* Determines where pdfs are saved  Use "Insert -> File Path..." to choose a file in the directory you want, then edit out the file name and leave the directory *)
writePdfs = False;  (* change to true if you want to save them.  Set the directory first!  If that SetDirectory command fails, the pdfs will still be saved in some default location that you might never find. *)

a = 1;
b = 1;
c = 0;
d = 2;
A = {{a,b},{c,d}};
{{lam2, lam1}, {evec2, evec1}} = Eigensystem[A];
v1 = 1.6 evec1/Norm[evec1];   (* The factor of 1.6 makes any unit vector long enough to be seen *)
v2 = 1.6 evec2/Norm[evec2];
vp = VectorPlot[{{a,b}, {c,d}}.{x,y},{x,-1,1},{y,-1,1},PlotLabel -> "A = "MatrixForm[A], PlotRange ->{{-1.1,1.1},{-1.1, 1.1}}];
evp = Graphics[{Thick,Cyan, Line[{-v1, v1}], Green, Line[{-v2, v2}]}];
evText = Graphics[{Cyan,Rectangle[{-1,1}, {-.3,.75}], Black, Text["(Subscript[λ, 1]) = "<>ToString[lam1], {-.65,.9},{0,0}], Green,Rectangle[{-1,.8}, {-.3,.6}], Black, Text["(Subscript[λ, 2]) = "<>ToString[lam2], {-.65,.7},{0,0}]}];
fig = Magnify[Show[vp, evp, vp, evText, ImageSize -> size/3], 3]
If[writePdfs, Export["eval12.pdf", fig, ImageSize -> size]]

a = 0;
b = 1;
c = 2;
d = -1;
A = {{a,b},{c,d}};
{{lam2, lam1}, {evec2, evec1}} = Eigensystem[A];
v1 = Sqrt[2] evec1/Norm[evec1];
v2 = Sqrt[2] evec2/Norm[evec2];
vp = VectorPlot[{{a,b}, {c,d}}.{x,y},{x,-1,1},{y,-1,1}, PlotLabel -> "A = "MatrixForm[A], PlotRange ->{{-1.1,1.1},{-1.1, 1.1}}];
evp = Graphics[{Thick,Cyan, Line[{-v1, v1}], Green, Line[{-v2, v2}]}];
evText = Graphics[{Cyan,Rectangle[{-1,1}, {-.3,.75}], Black, Text["(Subscript[λ, 1]) = "<>ToString[lam1], {-.65,.9},{0,0}], Green,Rectangle[{-1,.8}, {-.3,.6}], Black, Text["(Subscript[λ, 2]) = "<>ToString[lam2], {-.65,.7},{0,0}]}];
fig = Magnify[Show[vp, evp, vp, evText, ImageSize -> size/3], 3]
If[writePdfs, Export["eval1m2.pdf", fig, ImageSize -> size] ]

a = -2;
b = 1;
c = 2;
d = 1;
A = {{a,b},{c,d}};
{{lam2, lam1}, {evec2, evec1}} = Eigensystem[A];
If[Real[lam1 ], Print["real"]];
v1 = Sqrt[2] evec1/Norm[evec1];
v2 = Sqrt[2] evec2/Norm[evec2];
vp = VectorPlot[{{a,b}, {c,d}}.{x,y},{x,-1,1},{y,-1,1}, PlotLabel -> "A = "MatrixForm[A], PlotRange ->{{-1.1,1.1},{-1.1, 1.1}}];
evp = Graphics[{Thick,Cyan, Line[{-v1, v1}], Green, Line[{-v2, v2}]}];
evText = Graphics[{Cyan,Rectangle[{-1,1}, {-.3,.75}], Black, Text["(Subscript[λ, 1]) = "<>ToString[lam1//N], {-.65,.9},{0,0}], Green,Rectangle[{-1,.8}, {-.3,.6}], Black, Text["(Subscript[λ, 2]) = "<>ToString[lam2//N], {-.65,.7},{0,0}]}];
fig = Magnify[Show[vp, evp, vp, evText, ImageSize -> size/3], 3]
If[writePdfs, Export["evalirrat.pdf", fig, ImageSize -> size] ]

a = 1;
b = 2;
c = -2;
d = 1;
A = {{a,b},{c,d}};
{{lam1, lam2}, {evec1, evec2}} = Eigensystem[A];
v1 = Sqrt[2] evec1/Norm[evec1];
v2 = Sqrt[2] evec2/Norm[evec2];
vp = VectorPlot[{{a,b}, {c,d}}.{x,y},{x,-1,1},{y,-1,1}, PlotLabel -> "A = "MatrixForm[A], PlotRange ->{{-1.1,1.1},{-1.1, 1.1}}];
evText = Graphics[{Cyan,Rectangle[{-1,1}, {-.3,.75}], Black, Text["(Subscript[λ, 1]) = 1 + 2 i", {-.65,.9},{0,0}], Green,Rectangle[{-1,.8}, {-.3,.6}], Black, Text["(Subscript[λ, 2]) = 1 - 2 i", {-.65,.7},{0,0}]}];
fig = Magnify[Show[vp, evText, ImageSize -> size/3], 3]
If[writePdfs, Export["evalcomplex.pdf", fig, ImageSize -> size] ]

a = -1;
b = 1;
c = -2;
d = 1;
A = {{a,b},{c,d}};
{{lam1, lam2}, {evec1, evec2}} = Eigensystem[A];
v1 = Sqrt[2] evec1/Norm[evec1];
v2 = Sqrt[2] evec2/Norm[evec2];
vp = VectorPlot[{{a,b}, {c,d}}.{x,y},{x,-1,1},{y,-1,1}, PlotLabel -> "A = "MatrixForm[A], PlotRange ->{{-1.1,1.1},{-1.1, 1.1}}];
evText = Graphics[{Cyan,Rectangle[{-1,1}, {-.3,.75}], Black, Text["(Subscript[λ, 1]) = i", {-.65,.9},{0,0}], Green,Rectangle[{-1,.8}, {-.3,.6}], Black, Text["(Subscript[λ, 2]) = - i", {-.65,.7},{0,0}]}];
fig = Magnify[Show[vp, evText, ImageSize -> size/3], 3]
If[writePdfs, Export["evalimaginary.pdf", fig, ImageSize -> size] ]

The next cell needed to be modified.  There is only one eigenvector, and Mathematica returns evec2 = 0;

a = -1.5;
b = 1;
c = 0;
d = -1.5;
A = {{a,b},{c,d}};
{{lam1, lam2}, {evec1, evec2}} = Eigensystem[A];
If[Real[lam1 ], Print["real"]];
v1 = Sqrt[2] evec1/Norm[evec1];
evec2 = evec1; (* added for this cell only! *)
v2 = Sqrt[2] evec2/Norm[evec2];
vp = VectorPlot[{{a,b}, {c,d}}.{x,y},{x,-1,1},{y,-1,1}, PlotLabel -> "A = "MatrixForm[A], PlotRange ->{{-1.1,1.1},{-1.1, 1.1}}];
evp = Graphics[{Thick,Cyan, Line[{-v1, v1}]}];
evText = Graphics[{Cyan,Rectangle[{-1,1}, {-.3,.75}], Black, Text["(Subscript[λ, 1]) = "<>ToString[lam1], {-.65,.9},{0,0}], Green,Rectangle[{-1,.8}, {-.3,.6}], Black, Text["(Subscript[λ, 2]) = "<>ToString[lam2], {-.65,.7},{0,0}]}];
fig = Magnify[Show[vp, evp, vp, evText, ImageSize -> size/3], 3]
If[writePdfs, Export["evalrepeated.pdf", fig, ImageSize -> size] ]

a = 2;
b = -4;
c = 1;
d = -2;
A = {{a,b},{c,d}};
{{lam1, lam2}, {evec1, evec2}} = Eigensystem[A];
If[Real[lam1 ], Print["real"]];
v1 = Sqrt[2] evec1/Norm[evec1];
evec2 = evec1; (* added for this cell only! *)
v2 = Sqrt[2] evec2/Norm[evec2];
vp = VectorPlot[{{a,b}, {c,d}}.{x,y},{x,-1,1},{y,-1,1}, PlotLabel -> "A = "MatrixForm[A], PlotRange ->{{-1.1,1.1},{-1.1, 1.1}}];
evp = Graphics[{Thick,Cyan, Line[{-v1, v1}]}];
evText = Graphics[{Cyan,Rectangle[{-1,1}, {-.3,.75}], Black, Text["(Subscript[λ, 1]) = "<>ToString[lam1], {-.65,.9},{0,0}], Green,Rectangle[{-1,.8}, {-.3,.6}], Black, Text["(Subscript[λ, 2]) = "<>ToString[lam2], {-.65,.7},{0,0}]}];
fig = Magnify[Show[vp, evp, vp, evText, ImageSize -> size/3], 3]
If[writePdfs, Export["evalrepeated0.pdf", fig, ImageSize -> size] ]

a = 2;
b = 0;
c = 0;
d = 2;
A = {{a,b},{c,d}};
{{lam2, lam1}, {evec2, evec1}} = Eigensystem[A];
v1 = 1.6 evec1/Norm[evec1];   (* The factor of 1.6 makes any unit vector long enough to be seen *)
v2 = 1.6 evec2/Norm[evec2];
vp = VectorPlot[{{a,b}, {c,d}}.{x,y},{x,-1,1},{y,-1,1},PlotLabel -> "A = "MatrixForm[A], PlotRange ->{{-1.1,1.1},{-1.1, 1.1}}];
evp = Graphics[{Thick,Cyan, Line[{-v1, v1}], Green, Line[{-v2, v2}]}];
evText = Graphics[{Cyan,Rectangle[{-1,1}, {-.3,.75}], Black, Text["(Subscript[λ, 1]) = "<>ToString[lam1], {-.65,.9},{0,0}], Green,Rectangle[{-1,.8}, {-.3,.6}], Black, Text["(Subscript[λ, 2]) = "<>ToString[lam2], {-.65,.7},{0,0}]}];
fig = Magnify[Show[vp, evp, vp, evText, ImageSize -> size/3], 3]
If[writePdfs, Export["eval22.pdf", fig, ImageSize -> size]]

a = 0;
b = 1;
c = 0;
d = 0;
A = {{a,b},{c,d}};
{{lam1, lam2}, {evec1, evec2}} = Eigensystem[A];
If[Real[lam1 ], Print["real"]];
v1 = Sqrt[2] evec1/Norm[evec1];
evec2 = evec1; (* added for this cell only! *)
v2 = Sqrt[2] evec2/Norm[evec2];
vp = VectorPlot[{{a,b}, {c,d}}.{x,y},{x,-1,1},{y,-1,1}, PlotLabel -> "A = "MatrixForm[A], PlotRange ->{{-1.1,1.1},{-1.1, 1.1}}];
evp = Graphics[{Thick,Cyan, Line[{-v1, v1}]}];
evText = Graphics[{Cyan,Rectangle[{-1,1}, {-.3,.75}], Black, Text["(Subscript[λ, 1]) = "<>ToString[lam1], {-.65,.9},{0,0}], Green,Rectangle[{-1,.8}, {-.3,.6}], Black, Text["(Subscript[λ, 2]) = "<>ToString[lam2], {-.65,.7},{0,0}]}];
fig = Magnify[Show[vp, evp, vp, evText, ImageSize -> size/3], 3]
If[writePdfs, Export["evalfreeparticle.pdf", fig, ImageSize -> size] ]