# Cramer’s rule

Let $Ax=b$ be the matrix form of a system of $n$ linear equations in $n$ unknowns, with $x$ and $b$ as $n\times 1$ column vectors^{} and $A$ an $n\times n$ matrix. If $det(A)\ne 0$, then this system has a unique solution, and for each $i$ ($1\le i\le n$) ,

$${x}_{i}=\frac{det({M}_{i})}{det(A)}$$ |

where ${M}_{i}$ is $A$ with column $i$ replaced by $b$.

Title | Cramer’s rule |
---|---|

Canonical name | CramersRule |

Date of creation | 2013-03-22 11:55:27 |

Last modified on | 2013-03-22 11:55:27 |

Owner | akrowne (2) |

Last modified by | akrowne (2) |

Numerical id | 10 |

Author | akrowne (2) |

Entry type | Theorem |

Classification | msc 15A15 |