  The explicit formula for the elements of the successive intermediate matrices
of the Gauss-Jordan elimination procedure for the solution of systems of linear
equations is applied to error analysis. Stability conditions in terms of
relative uncertainty and size of determinants are given such that the
Gauss-Jordan procedure leads to a solution respecting the original imprecisions
in the right-hand member. The solution is the same as given by Cramer's Rule.
Imprecisions are modelled by scalar neutrices, which are convex groups of
(nonstandard) real numbers. The resulting calculation rules extend informal
error calculus, and permit to keep track of the errors at every stage.
