# Cramer rule

To solve $LaTeX: Ax=b$, where $LaTeX: A$ is nonsingular, the j-th coordinate is given by:
$LaTeX: x_j = \frac{ \mbox{det}(A^j)}{\mbox{det}(A)}$,
where $LaTeX: det(\cdot)$ is the determinant, and $LaTeX: A^j$ is the matrix obtained if column $LaTeX: j$ of $LaTeX: A$ is replaced by $LaTeX: b$:
$LaTeX: A^j = [A(., 1) A(., 2) \ldots A(., j-1) b A(., j+1), \ldots A(., n)]$.