a={{1,-1/2,-(i+2 j)/4,0,i/4,i/2+j},{-1/2,1/3,(n-2)/6,-(i+2 j)/4,0,(3 i-4 (n-2))/12},{-1/2,1/6,-(n-2)/12,(i+2 j-2 (n-2))/4,-(n-2)/12,-(3 i+2 (n-2))/12},{-1/2,1/6,j/4,0,-(2 i+j)/12,-j/2},{1/6,-1/6,-(n-2)/12,j/4,-(n-2)/36,-(n-2+2 i+j)/12},{1/3,-1/6,-(n-2)/12,(n-2-j)/4,(n-2)/36,(n-2+2 i+j)/12}};

MatrixForm[a]

d1=Det[a]

d2=Simplify[d1]

ContourPlot3D[d2==0,{n,0,4},{i,-2,2},{j,-2,2},AxesLabel->{"n","i","j"}]

d3=Simplify[41472d2/.n->2+z]

d4=Simplify[d3/.{i->x*z,j->y*z}]

d5=d4/z^4//Simplify

Plot3D[d5,{x,-3,3},{y,-3,3}]

p1=ContourPlot[d5,{x,0,2},{y,-0.5,1.5},Contours->{0}]

zz={};kk=0;

Dynamic[{kk,Union[zz]}]

a1=0;a2=2;b1=-1/2;b2=1;

Table[kk=k;
aa=a1+(a2-a1)*an/k;
bb=b1+(b2-b1)*bn/k;
dd=d5/.{x->aa,y->bb};
If[dd==0,AppendTo[zz,{aa,bb}];],{k,20},{an,k},{bn,k}];

zzz=Union[zz]

p2=ListPlot[zzz,PlotStyle->{Red,PointSize[Large]}]

Show[p1,p2]

a1=a /. {i->1,j->1,n->5}

Det[a1]

MatrixRank[a1]

a2=a /. {i->3,j->0,n->5}

Det[a2]

MatrixRank[a2]

a3=a /. {i->8,j->-1,n->8}

Det[a3]

MatrixRank[a3]

a4=a /. {i->4,j->3,n->19}

Det[a4]

MatrixRank[a4]