Question

does an M x N matrix have pivots less than or equal to m?

Answer 1

Answer:

Note that the rank of an m×n matrix cannot be bigger than m, since you can't have more than one pivot per row. It also can't be bigger than n, since you can't have more than one pivot per column. ... If m>n, then the rank is always less than m and there are at least m−n rows of zeroes in the reduced row-echelon