disp('Solution of the two-tank mixing problem via dsolve')
pause
[x y] = dsolve('Dx = (-1/3)*x + (1/12)*y + 1','Dy = (1/3)*x + (-1/3)*y + 2 ','t')
pause
disp('Let K1 = -C1 + 2*C2 and K2 = C1 + C2/4 so that')
disp('x = K1*(-1/2)*exp((-1/2)*t) + K2*(1/2)*exp((-1/6)*t')
disp('y = K1*exp((-1/2)*t) + K2*exp((-1/6)*t) ')
pause
disp('Eigenvectors and eigenvalues via eig')
pause 
A = [ -1/3 1/12; 1/3 -1/3]
[u d] = eig(A)
pause
disp('First column of u is an eigenvector with d(1,1) an eigenvalue')
pause
disp('A times column one')
A*u(:,1)
pause
disp('d(1,1) times column one')
d(1,1)*u(:,1)
pause
disp('column one times k = 1/u(2,1)')
u(:,1)/u(2,1)
pause
disp('Second column of u is an eigenvector with d(2,2) an eigenvalue')
pause
disp('A times column two')
A*u(:,2)
pause
disp('d(2,2) times column two')
d(2,2)*u(:,2)
pause
disp('column two times k = 1/u(2,2)')
u(:,2)/u(2,2)