Gauss Reduction is Non-Unique

Let us repeat the process of the last section, performing Gauss Reduction the long way. However, we will do things a little diferently, and thereby end up with a different form of the Row-Echelon matrix.

Here's the augmented matrix which we made previously:

> evalm(Ab);

Instead of swapping rows 1 and 2, let's swap rows 1 and 3:

> B2:=swaprow(Ab,1,3);

Next, we add row 1, multiplied by 1/2, to row 2, and replace row 2 with the result:

> B2:=addrow(B2,1,2,1/2);

Now we multiply row 2 by -2 in order to get rid of the fraction:

> B2:=mulrow(B2,2,-2);

Finally, we add row 2 to row 3 and replace row 3 with the result:

> B2:=addrow(B2,2,3,1);

This matrix "B2" is in Row-Echelon form, but it is not the same as obtained in the above section (matrix "B"). Let's compare the two matrices:

> evalm(B-B2);

They are definitely not the same, thereby confirming that Gauss Reduction is non-unique.

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