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Cramer rule

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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 [1]).

References

[1] G. Cramer, "Introduction à l'analyse des lignes courbes" , Geneva (1750) pp. 657
[2] A.G. Kurosh, "Higher algebra" , MIR (1972) (Translated from Russian)


Comments

References

[a1] T.M. Apostol, "Calculus" , 2 , Wiley (1969) pp. 93
How to Cite This Entry:
Cramer rule. I.V. Proskuryakov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Cramer_rule&oldid=14865
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098