# Determining linear independecy from rows

Normally when testing if two or more vectors are linearly independent, we would first put them in row echelon form and perform Gauss elimination on them.

Here are the vectors $[a_1, a_2, a_3]$, $[b_1, b_2, b_3]$ and $[c_1, c_2, c_3]$ in row echelon form, ready for Gauss elimination:

\begin{bmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2\\ a_3 & b_3 & c_3 \end{bmatrix}

Is it possible to determine if they are linearly independent by instead Gauss-eliminating the following matrix:

\begin{bmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3\\ c_1 & c_2 & c_3 \end{bmatrix}

Are the processes equivalent?