For any given 2 x 3 matrix, Why are only elementary steps allowed (i.e. aR1, R1 +/- R2, R1 <--> R2) and not any other operation (e.g. 3R1 + 2R2) when reducing the matrix to row echelon form? Also, is the operation R1 + R2 and R2 + R1 allowed simultaneously? I realize this would just output the exact same equation, which isn't incredibly useful, but is it allowed?