Find all linearly dependent subsets of this set of vectors I have vectors in such form
(1 1 1 0 1 0)
(0 0 1 0 0 0)
(1 0 0 0 0 0) 
(0 0 0 1 0 0) 
(1 1 0 0 1 0) 
(0 0 1 1 0 0) 
(1 0 1 1 0 0) 

I need to find all linear dependent subsets over $Z_2$.
For example 1,2,5 and 3,6,7.
EDIT (after @rschwieb)
The answer for presented vectors:
521
642
763
6541
7432
75431
765321
I did by brute force. I mean i wrote program to iterate through all variants in 
$${7 \choose 3} {7 \choose 4} {7 \choose 5} {7 \choose 6} {7 \choose 7}$$
99 in total.
But i just thought what some method exist for such task. For now im trying to implement http://en.wikipedia.org/wiki/Quadratic_sieve . Code incorporated in whole program. I plan to put it here then i organize it well.

Let us denote with $M$ (the transpose) of your matrix,
$$M= \begin{pmatrix}
1 & 0 & 1 & 0 & 1 & 0 & 1 \\
 1 & 0 & 0 & 0 & 1 & 0 & 0 \\
 1 & 1 & 0 & 0 & 0 & 1 & 1 \\
 0 & 0 & 0 & 1 & 0 & 1 & 1 \\
 1 & 0 & 0 & 0 & 1 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 
\end{pmatrix}.$$
As rschwieb already noted, a vector $v$ with $Mv=0$ solves your problem.
Using elementary row operation (modulo 2), we can easily bring it on the row echelon form
$$M' = \begin{pmatrix}
1 & 0 & 0 & 0 & 1 & 0 & 0 \\
 0 & 1 & 0 & 0 & 1 & 1 & 1 \\
 0 & 0 & 1 & 0 & 0 & 0 & 1 \\
 0 & 0 & 0 & 1 & 0 & 1 & 1 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
 0 & 0 & 0 & 0 & 0 & 0 & 0
\end{pmatrix}.$$
Now, it is easy to see that the vectors
$$v = \begin{pmatrix}
\alpha  \\
 \alpha +\beta +\gamma  \\
 \gamma  \\
 \beta +\gamma  \\
 \alpha  \\
 \beta  \\
 \gamma  \\
\end{pmatrix}
$$
parameterized by $\alpha$, $\beta$, $\gamma$ are in the kernel of $M'$ and thus in the kernel of $M$. Setting $\alpha =0,1$, $\beta=0,1$, and $\gamma=0,1$, we obtain the $2^3=8$ solutions. The solution with $\alpha=\beta=\gamma=0$ is trivial, so there are 7 nontrivial solutions.
