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