n=3, A=[2,1,-4;3,3,-5;4,5,-2], B=[8;14;16]
A(:,n+1) = B                           
A(2,:) = A(2,:) - A(1,:)*3/2              
A(3,:) = A(3,:) - A(1,:)*2                
A(3,:) = A(3,:) - A(2,:)*2                
X(3) = -4/4
X(2) = (2-X(3))/1.5                       
X(1) = (8 - A(1,2:3)*X(2:3))/2     

======================================================================= 

-->n=3, A=[2,1,-4;3,3,-5;4,5,-2], B=[8;14;16]
 n  =
 
    3.  
 A  =
 
!   2.    1.  - 4. !
!   3.    3.  - 5. !
!   4.    5.  - 2. !
 B  =
 
!   8.  !
!   14. !
!   16. !
 
-->A(:,n+1) = B                           
 A  =
 
!   2.    1.  - 4.    8.  !
!   3.    3.  - 5.    14. !
!   4.    5.  - 2.    16. !
 
-->A(2,:) = A(2,:) - A(1,:)*3/2              
 A  =
 
!   2.    1.   - 4.    8.  !
!   0.    1.5    1.    2.  !
!   4.    5.   - 2.    16. !
 
-->A(3,:) = A(3,:) - A(1,:)*2                
 A  =
 
!   2.    1.   - 4.    8. !
!   0.    1.5    1.    2. !
!   0.    3.     6.    0. !
 
-->A(3,:) = A(3,:) - A(2,:)*2                
 A  =
 
!   2.    1.   - 4.    8. !
!   0.    1.5    1.    2. !
!   0.    0.     4.  - 4. !
 
-->X(3) = -4/4
 X  =
 
!   0. !
!   0. !
! - 1. !
 
-->X(2) = (2-X(3))/1.5                       
 X  =
 
!   0. !
!   2. !
! - 1. !
 
-->X(1) = (8 - A(1,2:3)*X(2:3))/2     
 X  =
 
!   1. !
!   2. !
! - 1. !