Matrix gauss continuation Suppose we have the matrix $4\times4$, $R_1 =(0,0,1,1)$, $R_2=(0,1,1,0)$, $R_3=(1,1,0,0)$, $R_4(1,0,0,0)$ and suppose we want to see the rank.The difficult part is that you cannot order them somehow to use gauss.Any ideas what should be done in such situations?

You can subtract any row from any other without changing the rank:
$$\begin{pmatrix}0&0&1&1\\0&1&1&0\\1&1&0&0\\1&0&0&0\end{pmatrix}\sim\begin{pmatrix}0&0&1&1\\0&1&1&0\\0&1&0&0\\1&0&0&0\end{pmatrix}\sim\begin{pmatrix}0&0&1&1\\0&0&1&0\\0&1&0&0\\1&0&0&0\end{pmatrix}\sim\begin{pmatrix}0&0&0&1\\0&0&1&0\\0&1&0&0\\1&0&0&0\end{pmatrix}$$
So the rank is full.
You can also reorder the rows at the beginning as this doesn't change the rank:
$$\begin{pmatrix}1&0&0&0\\1&1&0&0\\0&1&1&0\\0&0&1&1\end{pmatrix}$$
and continue as before.
