I am trying to understand how to determine the linear dependence/independence of a set of complex vectors.  I know the process is the same as determining linear dependence/independence of a set of real vectors, but I am a little confused on how to augment the sets of vectors.  For instance if I have
$$
\begin{bmatrix} 2 + i \\ 1 \end{bmatrix}, \begin{bmatrix} 1 \\ 1 - i \end{bmatrix}
$$
I know when expanded out into the real and complex parts I have
$$
\begin{bmatrix} 2 \\ 1 \end{bmatrix} + i\begin{bmatrix} 1 \\ 0 \end{bmatrix} , \begin{bmatrix} 1 \\ 1 \end{bmatrix} + i\begin{bmatrix} 0 \\ -1 \end{bmatrix}
$$
For the augmented matrix do I just use the original set of vectors like the following?
$$
\left[\begin{array}{cc|c} 2 + i &amp; 1 &amp; 0\\ 1 &amp; 1 - i &amp;0\end{array}\right]
$$
or do I some how have to use the expanded set of vectors?

Any help would be greatly appreciated.


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