Read the result
The recommended pivot is the largest available entry by magnitude, not necessarily the positive one.
Numerical stability
Pivoting Explainer
Pick the best pivot row by comparing absolute values in the active column.
Formula
choose the candidate row with the largest absolute pivot entry
Result
Worked substitution
Pivoting reduces the damage caused by dividing by very small numbers during elimination.
Where it helps
Use it before elimination when a pivot is zero or much smaller than another entry below it.
Common slip
A tiny non-zero pivot can be mathematically valid but numerically poor.
Try it
Make all three candidate pivots 0. The tool should warn that this column cannot supply a pivot.