Linear Algebra - Basis for a row space

A =
Code:
 1  2 -1  3
3  5  2  0
0  1  2  1
-1  0 -2  7

Problem: Find a basis for the row space of A consisting of vectors that are row vector of A.

My attempt:

I transpose the matrix A and put it into reduced row echelon form. It turns out that there are leading ones in every column. Therefore, the basis includes every row vector from A.

Is this the correct way to handle this problem?