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Gaussian elimination technique (and its different refinements) is essentially
the numerical method of choice for the built-in algorithms of numerical soft-
wares, including MATLAB. The following two examples are essential build-
ing blocks in such constructions.

Example 8.4
Without using the MATLAB inverse command, solve the system of equations:

LX = B (8.12)
where L is a lower triangular matrix.

Solution: In matrix form, the system of equations to be solved is

L  0 0 L 0  x   b  
1
 11   1   
 L 21 L 22 0 L 0   x 2   b 2 
 M M M O M   M  =   (8.13)
M
     
M
 M M M L M   M   
 L  n1 L n2 L n3 L L   x   b  
n
n
nn 
The solution of this system can be directly obtained if we proceed iteratively.
That is, we find in the following order: x , x , …, x , obtaining:
1
n
2
b
x = 1
1
L
11
x = ( b − L x )
21 1
2
2
L
22
(8.14)
M
 k 1 
−
k ∑
 b − L x 
 kj j 
=
x =  j 1 
k
L
kk
The above solution can be implemented by executing the following script
M-file:
L=[ ]; % enter the L matrix
b=[ ]; % enter the B column
n=length(b);
x=zeros(n,1);

© 2001 by CRC Press LLC