The Gauss-Jordan Method is Unique

In the above section entitled "Gauss Reduction is Non-Unique", we found an alternate Row-Echelon form of the augmented matrix, called "B2", which is not the same as "B". In this section we continue with the row operations on matrix "B2" to get a Reduced Row-Echelon matrix "C2" which will be the same as "C" obtained above.

> C2:=mulrow(B2,3,-1/2);

> C2:=addrow(C2,3,2,4);

> C2:=addrow(C2,3,1,-2);

> C2:=addrow(C2,2,1,-5);

> C2:=mulrow(C2,1,-1/4);

Let's now compare this to "C" obtained in the preceding section:

> evalm(C-C2);

Indeed, C2 is the same as C, thereby verifying that although Gauss Reduction is non-unique, the full Gauss-Jordan Method does lead to unique results.

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