ESc101N Laboratory Assignment
                      Wednesday of week of 16/8/04

PROBLEM: Write a program (with one class and that too having only the 
"main" method) to compute the solution of system of linear eqautions 
with 3 variables using Gaussian Elimination. You may assume that a 
unique solution exists.


Details:

1) Use InputBox and OutBox Classes of Package javabook for taking input from the user 
and for displaying results.


2) Method : 

(a11)x + (a12)y + (a13)z = c1  ... (1)
(a21)x + (a22)y + (a23)z = c2  ... (2)
(a31)x + (a32)y + (a33)z = c3  ... (3)


Reduce eqns (1)and (2)to linear equations in 2 variables using the following steps :-
	a) Multipy eqn(1) by (a21)
	(a21) * [(a11)x + (a12)y + (a13)z] = (a21) * c1  ... (4)

	b) Multipy eqn(2) by (a21)
	(a11) * [(a21)x + (a22)y + (a23)z] = (a11) * c2  ... (5)

	c) Subtract eqn(5) from eqn(4)
	[(a21)*(a12) - (a11)*(a22)]y + [(a21)*(a13)-(a11)*(a23)]z = (a21)*c1 - (a11)*c2  ... (6)

Similarly reduce, eqns (2) and (3) to linear equations in 2 variables to get the following eqn. :
[(a31)*(a22) - (a21)*(a32)]y + [(a31)*(a23)-(a21)*(a33)]z = (a31)*c2 - (a21)*c2 ... (7)

Now, solve eqns. (6) and (7) again by Gaussian Elimination to get the values of y and z

and by putting these values in (1), (2) or (3), get the value of x.

3) Note that the initial coefficients (a11, ... a33) are integers. When solving for values of x,
y, and z, the results may be floating point. So, use float or double variable to store them.