% Himmelblau & Riggs 7th ed, Workbook problem 7.4
% example of solution of simultaneous algebraic equations
%
% from compenent balances
% 0.8 F - 0.8 wBF - 0.109 W = 350
% 0.2 F - 0.2 wBF - 0.217 W = 0
%             wBF - 0.674 W = 0
%
% write in the matrix form
% a*x = b
% a is coefficient matrix
% x is unknown vector = [F; wBF; W] (column vector)
% b is constant vector (column vector)

% when entering matrix row elements, can separate with space or comma
% when starting new matrix row, can terminate previous row with
% new line (see entry of a below) or semicolon (see entry of b below)
% semicolon at end of line of code suppresses screen echo of result

a = [0.8 -0.8 -0.109
0.2 -0.2 -0.217
0 1 -0.674];

b = [350; 0; 0]

fprintf('solution using x = inv(a)*b')

x = inv(a)*b

fprintf('check result')

bp = a*x

% alternatively use backslash operator
% which also estimates answer with overdetermined systems

fprintf('solution using x = a\\b')

x = a\b % note backslash