Cramer's rule

Cramer's rule is a formula for finding the value of an unknown given a system of linear equations. For the system

$AX=B$

$x_i=\frac{|A_i|}{|A|}\qquad i=1,\ldots,n$

where $x_i$ is the $i$^th variable in the system and $A_i$ is the matrix formed by replacing the $i$^th column of $A$ with $B$ . This will not work if the determinant of $A$ is zero; in this case, there will be an infinite number of solutions.