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.

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