%% Annotated Matlab transcript -- 4/24
%% CS 323 - Doug DeCarlo

% Solving Ax = b

A = [1 1 -2; 1 1 1; 1 -1 0]
% this needs to be a column vector -- hence the '
b = [3 1 2]';

% Matlab's way of solving linear systems
A \ b
% you can do it this way to, but it's a lot slower as it builds the inverse
inv(A) * b

% If b is of this form, we can see how the method for buildling the
% inverse works...
b = [1 0 0]'
format short
inv(A)
A \ b

% LU decomposition is built in, where P is the permutation matrix
% so that LU = PA
[L,U,P] = lu(A)
% we can reconstruct A this way
inv(P)*L*U
A