% 
% Written by:
% -- 
% John L. Weatherwax                2009-04-21
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; drawnow; clear functions; 
rehash; 
clc; 

format rat;

% Part (a):
M = [ 1, 0, 0 ; 0, 0, -1; 0, 1, 0 ]; 
L = inv(M) 

% Part (b): 
M = [ 1, 0, 0, 0 ; -1, 1, 0, 0 ; 0, 0, 0, -1 ; 0, 0, 1, 0 ];
L = inv(M)

% Part (c): 
M = [ 1  , 0 , 0 , 0 , 0 , 0 ; 
      -1 , 1 , 0 , 0 , 0 , 0 ; 
      0  , 0 , 0 , -1 , 0 , 0 ; 
      0 , 0 , 1 , 0 , 0 , 0 ; 
      0 , 0 , 0 , 1 , 0 , -1 ; 
      0 , 0 , -1 , 0 , 1 , 0 
];
L = inv(M)

% Part (d): 
M = [ 1  , 0 , 0 , 0 , 0 , 0 ; 
      -1 , 1 , 0 , 0 , 0 , 0 ; 
      0  , 0 , sqrt(3)/2 , -1/2 , 0 , 0 ; 
      0 , 0 , 1/2 , sqrt(3)/2 , 0 , 0 ; 
      0 , 0 , 0 , 0 , 1/2, -sqrt(3)/2 ; 
      0 , 0 , 0 , 0 , sqrt(3)/2 , 1/2 
];
L = inv(M)