1 1 1
4 1 2
0 0 0
1 1 1
6 1 3
0 0 0
1 1 1
5 1 4
0 0 0
1 1 1
3 1 5
1 1 0
0 0 0
0 0 0

Equations:

x_1 + 4 x_2 = 0
x_1 + 6 x_3 = 0
x_1 + 5 x_4 = 0
x_1 + 3 x_5 + 1 = 0