# 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 $\det(A)\neq 0$, then this system has a unique solution, and for each $i$ ($1\leq i\leq n$) ,

 $x_{i}=\frac{\det(M_{i})}{\det(A)}$

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

Title Cramer’s rule CramersRule 2013-03-22 11:55:27 2013-03-22 11:55:27 akrowne (2) akrowne (2) 10 akrowne (2) Theorem msc 15A15