CRAMER`S RULE
=============

If we have a system of equations such as:

	a11 x1 + a12 x2 = C1
	a21 x1 + a22 x2 = C2

Where the a terms are constants and the C terms are either constants of functions, we may extract solutions for x1 & x2 by means of _Cramer`s Rule_.

If we form the matrixes:

	[ a11 a12 ]     [ C1 ]
	[ a21 a22 ]     [ C2 ]

Then it has been shown that, for there to be a unique solution, then the determinant of the coefficient matrix (on the left above) must be non zero.  If this is the case, then Cramer`s Rule tells us that if we wish to determine x1, then we replace the x1 coefficients in the first matrix by the C terms from the second matrix, take the determinant of this new matrix and divide by the determinant of the original matrix (which is why it must be nonzero).  In mathematical notation, we write that:

	     | C1  a12 |
	     | C2  a22 |
	x1 = -----------
	     | a11 a12 |
	     | a21 a22 |

And, similarly,

	     | a11  C1 |
	     | a21  C2 |
	x2 = -----------
	     | a11 a12 |
	     | a21 a22 |


The same principal may be applied to larger systems of equations.





As usual, no guarantees are made as to the accuracy or obsolescence of this information.  Use at your own risk.