# Cramer rule

From Encyclopedia of Mathematics

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