Work out row echelon form instantly with clear inputs, formula shown and shareable results.
Row reduction uses row swaps, scaling and subtraction to create leading ones with zeros below. The number of pivots is the rank, and the remaining columns correspond to free variables.
Rank-nullity
rank + number of free columns = total columns
The third row is the sum of the first two, so it reduces away and the rank is 2 with two free columns.
No. They preserve the row space, which is exactly why elimination is a valid way to find the rank.