Talk:Cramer's rule

When did Gabriel Cramer come up with Cramer's Rule?

ANS: Around 1750, two years before his death. He died without giving an explanation of how exactly he came up with the rule. There is some speculation that Colin Maclaurin came up with the same rule in 1729 but there must have been a paper shortage in Scotland because it was never published until after he died.

More precise statement

Any chance someone is willing to give a more precise statement of Cramer's rule? As in the following: Let R be a commutative ring, M a finitely generated R-module with generators $m_{i}$, and $\phi :M\rightarrow M$ an endomorphism of R-modules. $\phi$ determines a matrix

$A=(a_{ij})$

via $\phi (m_{i})=\sum a_{ij}m_{j}$. Then Adj(A)A=det(A)I, where Adj(A) is the cofactor matrix of A.