Cramer's rule

Cramer's rule is a theorem in linear algebra, which gives the solution of a system of linear equations in terms of determinants. It is named after Gabriel Cramer (1704 - 1752).

Abstract formulation

Let R be a commutative ring, A an n×n matrix with coefficients in R. Then

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:Adj(A)A = det(A)I

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

where Adj(A) denotes the adjugate of A, det(A) is the determinant, and I is the identity matrix.

Related Topics:
Adjugate - Identity matrix

~ ~ ~ ~ ~ ~ ~ ~ ~ ~