# Reduced row echelon form

If A is a 3 x 5 matrix, then the number of leading 1’s in its reduced row echelon form is at most _____. Explain your solution.

-
have you tried anything ? –  Dominic Michaelis Feb 19 '13 at 23:15
Seriously?............. –  gnometorule Feb 19 '13 at 23:15
Really?........... –  user60610 Feb 19 '13 at 23:18
I want to say 3 but I'm not sure how to explain myself. –  shaya Feb 19 '13 at 23:21
try to explain it –  Dominic Michaelis Feb 19 '13 at 23:23
There is at most one such $1$ per row. There are $3$ rows. So it is at most $3$.
Moreover, you can easily construct an example where it is exactly $3$, so $3$ is sharp.