Math 202


An example of a homogeneous linear system arising in chemistry:
---------------------------------------------------------------


The augmented matrix appears below:

 2 	 0 	-1 	-1 	 0 	 0 	
 1 	 0 	 0 	 0 	-1 	 0 	
 3 	 0 	 0 	-3 	-2 	 0 	
 0 	 2 	-1 	-1 	 0 	 0 	

Matrix number 1 appears below:

 1 	 0 	-1/2 	-1/2 	 0 	 0 	
 1 	 0 	 0 	 0 	-1 	 0 	
 3 	 0 	 0 	-3 	-2 	 0 	
 0 	 2 	-1 	-1 	 0 	 0 	

Matrix number 2 appears below:

 1 	 0 	-1/2 	-1/2 	 0 	 0 	
 0 	 0 	 1/2 	 1/2 	-1 	 0 	
 3 	 0 	 0 	-3 	-2 	 0 	
 0 	 2 	-1 	-1 	 0 	 0 	

Matrix number 3 appears below:

 1 	 0 	-1/2 	-1/2 	 0 	 0 	
 0 	 0 	 1/2 	 1/2 	-1 	 0 	
 0 	 0 	 3/2 	-3/2 	-2 	 0 	
 0 	 2 	-1 	-1 	 0 	 0 	

Matrix number 4 appears below:

 1 	 0 	-1/2 	-1/2 	 0 	 0 	
 0 	 0 	 1/2 	 1/2 	-1 	 0 	
 0 	 0 	 3/2 	-3/2 	-2 	 0 	
 0 	 1 	-1/2 	-1/2 	 0 	 0 	

Matrix number 5 appears below:

 1 	 0 	-1/2 	-1/2 	 0 	 0 	
 0 	 1 	-1/2 	-1/2 	 0 	 0 	
 0 	 0 	 3/2 	-3/2 	-2 	 0 	
 0 	 0 	 1/2 	 1/2 	-1 	 0 	

Matrix number 6 appears below:

 1 	 0 	-1/2 	-1/2 	 0 	 0 	
 0 	 1 	-1/2 	-1/2 	 0 	 0 	
 0 	 0 	 1 	-1 	-4/3 	 0 	
 0 	 0 	 1/2 	 1/2 	-1 	 0 	

Matrix number 7 appears below:

 1 	 0 	 0 	-1 	-2/3 	 0 	
 0 	 1 	-1/2 	-1/2 	 0 	 0 	
 0 	 0 	 1 	-1 	-4/3 	 0 	
 0 	 0 	 1/2 	 1/2 	-1 	 0 	

Matrix number 8 appears below:

 1 	 0 	 0 	-1 	-2/3 	 0 	
 0 	 1 	 0 	-1 	-2/3 	 0 	
 0 	 0 	 1 	-1 	-4/3 	 0 	
 0 	 0 	 1/2 	 1/2 	-1 	 0 	

Matrix number 9 appears below:

 1 	 0 	 0 	-1 	-2/3 	 0 	
 0 	 1 	 0 	-1 	-2/3 	 0 	
 0 	 0 	 1 	-1 	-4/3 	 0 	
 0 	 0 	 0 	 1 	-1/3 	 0 	

Matrix number 10 appears below:

 1 	 0 	 0 	 0 	-1 	 0 	
 0 	 1 	 0 	-1 	-2/3 	 0 	
 0 	 0 	 1 	-1 	-4/3 	 0 	
 0 	 0 	 0 	 1 	-1/3 	 0 	

Matrix number 11 appears below:

 1 	 0 	 0 	 0 	-1 	 0 	
 0 	 1 	 0 	 0 	-1 	 0 	
 0 	 0 	 1 	-1 	-4/3 	 0 	
 0 	 0 	 0 	 1 	-1/3 	 0 	

Matrix number 12 appears below:

 1 	 0 	 0 	 0 	-1 	 0 	
 0 	 1 	 0 	 0 	-1 	 0 	
 0 	 0 	 1 	 0 	-5/3 	 0 	
 0 	 0 	 0 	 1 	-1/3 	 0