"Do we use “Row echelon form” or “Redueced Row echelon form” in order to find a basis for “Row space”? For problem3, question 4"

• Yes you can switch rows. As long as you arrive at an echelon form you use the linearly independent non-zero rows to make a basis.
• We can use reduced row echelon form or just regular row echelon form to make the basis. All that matter is that the row vectors are linearly independent.