If the determinant of a square system of linear equations
does not vanish, then the system has a unique solution. This solution is given by the formulas
Here is the determinant obtained from when the -th column is replaced by the column of the free terms . Formulas (*) are known as Cramer's formulas. They have been found by G. Cramer (see ).
|||G. Cramer, "Introduction à l'analyse des lignes courbes" , Geneva (1750) pp. 657|
|||A.G. Kurosh, "Higher algebra" , MIR (1972) (Translated from Russian)|
|[a1]||T.M. Apostol, "Calculus" , 2 , Wiley (1969) pp. 93|
Cramer rule. I.V. Proskuryakov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Cramer_rule&oldid=14865