kill(all)$

van=facebook.com/LearningCalculus$

     Magic Squares 4 x 4 Case

M: matrix(
    [a,b,c,d,0,0,0,0,0,0,0,0],
    [e,f,g,h,0,0,0,0,0,0,0,0],
    [i,j,k,l,0,0,0,0,0,0,0,0],
    [m,n,o,p,0,0,0,0,0,0,0,0],
    [0,0,0,0,a,e,i,m,0,0,0,0],
    [0,0,0,0,e,f,g,h,0,0,0,0],
    [0,0,0,0,i,j,k,l,0,0,0,0],
    [0,0,0,0,m,n,o,p,0,0,0,0]
);

rhs:matrix([s],[s],[s],[s]);

first(fullratsimp(linsolve_by_lu(M,rhs)));