clear
disp('Block Gauss elimination')
disp('Generate a random 5x5 matrix')
disp('Caution:  it may not have an inverse')
A = rand(5)
pause
A11 = A(1:2,1:2)
pause
A12 = A(1:2,3:5)
pause
A21 = A(3:5,1:2)
pause
A22 = A(3:5,3:5)
pause
d = [1 2 3 4 5]'
pause
d1 = d(1:2)
pause
d2 = d(3:5)
pause
disp('sol1 = A\d')
sol1 = A\d
pause
disp('sol2 = inv(A)*d')
sol2 = inv(A)*d
pause
disp('Schur complement via block row operation')
A22hat  = A22 - A21*inv(A11)*A12
pause
d2hat = d2 - A21*inv(A11)*d1
pause
disp('Solution via block backward substitution')
x2 = inv(A22hat)*d2hat;
x1 = inv(A11)*(d1 - A12*x2);
disp('sol3 via block Gauss-El.')
sol3 =[x1;x2]