I understand that when solving for a linear dep/independent matrix, you can take the determinant of the matrix and if it is zero, then it is linearly dependent. However, how can I go about doing this for something like two $3\times 1$ vectors?

Example:

$$\begin{bmatrix} -6 \\ -1 \\ -7 \end{bmatrix}, \begin{bmatrix} -1 \\ -5 \\ 4\end{bmatrix} $$

The RREF yield infinitely many solutions, because R3 0=0. Does this tell me that the system is linearly independent if it has infinitely many solutions?