Sort each matrix by whether it is in row echelon form. Each row's leading entry must sit strictly to the right of the one above, and zero rows must sink to the bottom.

In row echelon form: rows (1, 2, 3), (0, 1, 4), (0, 0, 5), rows (1, 0, 0), (0, 1, 0), (0, 0, 1), rows (2, 1), (0, 0)

Not in row echelon form: rows (1, 2, 3), (0, 0, 0), (0, 1, 4), rows (0, 1, 2), (1, 0, 3)

m1, m4 and m5 have leading entries marching strictly rightward with any zero row at the bottom. m2 places a zero row above a nonzero one. In m3 the second row's leading entry is in column 1, to the LEFT of the first row's in column 2, a swap would fix it. Note that pivots need not equal 1 for plain echelon form.