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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 ith variable in the system and A_i is the matrix formed by replacing the ith 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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