CramersRule 2001-10-29 19:56:24 2002-09-21 15:03:25 Theorem \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} 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 $b$.