%-----------------------------------------------------------------------
% Use "inv", "\" (pre-division), or "^-1", to solve a set of linear algebraic equations in MATLAB
%   Ax=b
% A minimum hard-coded example; not recommended.
% Instructor: Nam Sun Wang
%-----------------------------------------------------------------------

% Start fresh ----------------------------------------------------------
      clear all

% Input matrix/vector coefficients from the problem discussed in class
%     3*x1 -   x2 + 2*x3 = 12
%       x1 + 2*x2 + 3*x3 = 11
%     2*x1 - 2*x2 -   x3 =  2
% The coefficients for matrix A are (in row-wise order):
      A = [ 3 -1 2 ; 1 2 3 ; 2 -2 -1 ];
% The coefficients for column vector b are:
      b = [ 12; 11; 2 ];

% Solve the linear set of equations by calling the "inv" function ------
      x = inv(A)*b;

% Print results --------------------------------------------------------
      disp('The solution with the "inv" function is ...')
      disp(x)

% An alternative way by pre-division -----------------------------------
      x = A\b;

% Print results --------------------------------------------------------
      disp('The solution with pre-division is ...')
      disp(x)

% Yet another way by raising to -1 power  ------------------------------
      x = A^(-1)*b;

% Print results --------------------------------------------------------
      disp('The solution with ^-1 is ...')
      disp(x)