Dictionary:Cramer’s rule

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{{#category_index:C|Cramer’s rule}} (krā’ m∂rz) The solution to a set of linear equations in unknowns written compactly as


has solutions for each given by the ratio of determinants

where the matrix is obtained by replacing the -th column of the matrix with the vector b.

This is usually not the most economical way for computers to solve simultaneous equations. Named for Gabriel Cramer (1704–1752), French mathematician.