In
linear algebra,
Cramer's rule is an explicit formula for the solution of a
system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the
determinants of the (square) coefficient
matrix and of matrices obtained from it by replacing one column by the vector of right hand sides of the equations. It is named after
Gabriel Cramer (1704–1752), who published the rule for an arbitrary number of unknowns in 1750, although
Colin Maclaurin also published special cases of the rule in 1748 (and possibly knew of it as early as 1729).