Hi guys,

I am trying to solve a set of equations which have matrices (The code for that is at the bottom). Solutions are of this form

{{k[1][2] -> 1 - k[1][1], k[2][2] -> 1 - k[2][1]}}

{{k[1][2] -> -3 + k[1][1], k[2][2] -> 3 + k[2][1]}}

Is there any way I can re-use these solutions to convert them in the form of equations as k[1][2]= 1 - k[1][1], as I intend to use these linear equation further for solving under constraints using Reduce:

Reduce[{Sol1[[1, 1]] && Sol1[[1, 2]] && Sol2[[1, 1]] && Sol2[[1, 2]] && 0.9 <= m11 <= 1.1 && 0.9 <= m22 <= 1.1}, {k[1][1], k[1][2], k[2][1], k[2][2]}]

but as: {{k[1][2] -> 1 - k[1][1], k[2][2] -> 1 - k[2][1]}} or {{k[1][2] -> -3 + k[1][1], k[2][2] -> 3 + k[2][1]}} these are rules not equations, therefore I am unable to solve them automatically by excessing in this way "Sol1[[1, 1]]". Is there any way I can treat these rules -> as equations so that I can further use it for Reduce procedure?

(you can copy paste the bellow code to execute).

Thanks

Usman

ClearAll;

K=Table[k[i][i],{i,1,2},{j,1,2}];

M=Table[m[i][i],{i,1,2},{j,1,2}];

Psi=Table[psi[i][i],{i,1,2}];

m[1][2]=0;

m[2][1]=0;

M//MatrixForm;

Psi//MatrixForm;

Sol1=Solve[K.Psi==(W^2*M).Psi/.{W->Sqrt[1],psi[1]->1,psi[2]->1,m[1][1]->1,m[2][2]->1},{k[1][1],k[1][2],k[2][1],k[2][2]}]

Sol2=Solve[K.Psi==(W^2*M).Psi/.{W->Sqrt[3],psi[1]->1,psi[2]->-1,m[1][1]->1,m[2][2]->1},{k[1][1],k[1][2],k[2][1],k[2][2]}]