I know that to find whether vectors are independent, you make them the columns of a vector and rref. For example, (1, 2, 4, 5) (2, 3, 4, 7) and (2, 4, 2, 4) become
\begin{bmatrix} 1 & 2 & 2 \\\\ 2 & 3 & 4 \\\\ 4 & 4 & 2 \\\\ 5 & 7 & 4 \end{bmatrix}
From here, I rref the matrix to see if the vectors are independent or not. If there is more than one row of zeros, then the vectors are dependent.
However, if I were to transpose the matrix, can I still use the same method as a test for independence?
\begin{bmatrix} 1 & 2 & 4 & 5 \\\\ 2 & 3 & 4 & 7\\\\ 2 & 4 & 2 & 4 \end{bmatrix}
This time, if the rref creates any rows of zeros, OR if the final column is nonzero, the vectors would be dependent. Is this a valid method since the rank of a matrix is equal to the rank of its transpose?