% This code illustrates row operations and
% Gauss elimination.
disp('Solution of Ax = d via Gauss elimination')
disp('Press a key to continue,')
A = [2 6 8;4 15 19;2 0 3]
pause
d = [ 16 38 6]'
pause
Aug_mat = [A d]
pause
E21 = eye(3);
E21(2,1) = -2
pause
disp('E21 [A d] = ')
disp(E21*[A d])
pause
E31 = eye(3);
E31(3,1) = -1
pause
disp('E31 (E21 [A d]) = ')
disp(E31*E21*[A d])
pause
E32 = eye(3);
E32(3,2) = 2
pause
disp('E32 (E31 (E21 [A d])) = ')
disp(E32*E31*E21*[A d])
UU = E32*E31*E21*[A d]
disp('This completes the row operation step of Gauss-El.')
pause
disp('The backward substitution step can be done by \')
pause
disp('UU(1:3,1:3)\UU(1:3,4)')
pause
sol = UU(1:3,1:3)\UU(1:3,4)
disp('Also \ can do both steps of Gauss-El.')
disp('A\d')
pause
sol = A\d
pause
disp('The solution of the steady-state two mixing tank is as follows:')
Atank = [-1/3 1/12; 1/3 -1/3]
pause
dtank = [-1 -2]'
pause
disp('soltank = Atank\dtank  ')
soltank = Atank\dtank
pause
disp('The solution of the two loop resistor ciruit is as follows:')
disp('Let R1 = 1, R2 = 2 , R3 = 3, E1 = 10 and E2 = 20.')
Acircuit = [1 -1 1;1 0 -3;0 -2 -3]
pause
dcircuit = [0 10 20]'
pause
disp('solcircuit = Acircuit\dcircuit  ')
solcircuit = Acircuit\dcircuit
pause
disp('The solution of single node structure is as follows:')
theta = pi/6
c = cos(theta);
s = sin(theta);
Anode1 = [c 1; -s 0]
pause
dnode1 = [0 -100]'
pause
disp('solnode1 = Anode1\dnode1  ')
solnode1 = Anode1\dnode1