%
% - File name : linear_2.m (Generated by Hee Jung : fall/1999)
% - Solve linear algebric equations using MATLAB's backslash(\) command
% - Sources of help on this command can be found from:
% 1) Pratap's MATLAB 5 book
% 2) type help mldivide in the matlab command window
%
% - Problem to solve: find the solution of following set of linear equations
% 3* x1 + 5* x2 + 2* x3 = 3
% x1 + 7* x3 = 2
% x2 + 3* x3 = 5
% - How to solve?
% : express system of linear equations in the form of Ax = b and then
% solve with \ command in matlab.
%
% - The only difference between the approach here and in 'linear_1.m' is the
% way A matrix is constructed. The approach used here is good if the matrix
% A has lots of zeros.
%
clear % removes all variables from the workspace
% Predefine A matrix as zero matrix.
A = zeros(3,3); % A = zeros(3) would also work.
% Enter the element of A matrix which is not zero.
A(1,[1, 2, 3]) = [3, 5, 2];
A(2,[1, 3] ) = [1, 7];
A(3,[2, 3] ) = [1, 3];
% The above command will generate A = [3 5 2; 1 0 7; 0 1 3]
% Define B vector
b = [3;2;5];
% Solve the problem using backslash. you type :
x = A\b
% You'll get
% x = [-3.7647; 2.5294; 0.8235]
% that means x1 = -3.7647, x2 = 2.5294, x3 = 0.8235
% Check the solution by typing
A*x - b
% and note that you get Matlabs attempt at saying [ 0 0 0 ]'.