* ======================================================================= 
*  File:  	matrix 002.SPS .
*  Date:  	24-Oct-2003 .
*  Author:  	Bruce Weaver, weaverb@mcmaster.ca .
*  Notes:	Use matrix language to solve system of simultaneous
		linear equations .
* ======================================================================= .

* The following example is taken from Appendix A of "Mathematical Statistics
* with Applications" (2nd Ed.) by Mendenhll, Scheaffer, & Wackerly ISBN 0-8710-410-3).

* The 3 equations in the system of equations are:
*	2(v1) + v3 = 4.
*	v1 - v2 + 2(v3) = 2.
* 	v1 = 1.

* Matrix A is used to represent the coefficients by which v1, v2, and v3 are multiplied.
* Matrix G is used to hold the results of the 3 equations (i.e., 4, 2, and 1).

matrix.
compute a = 
{2, 0, 1;
 1, -1, 2;
 1, 0, 0}.
compute g = {4; 2; 1}.
compute v = inv(a)*g.
print a /title = 'Matrix A'.
print inv(a) /title = 'Inverse of A'.
print v /title = 'Matrix V'.
print /title = 'So v1 = 1, v2 = 3, and v3 = 2.'.
end matrix.

* ======================================================================= .