Cramer rule

From Glossary

Jump to: navigation, search

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)].

Personal tools