[pzhon]

2*v1=(0,0,0,0). That's trivial, since 2=0 in your scalar field.

You're looking for a nontrivial linear dependence between v1, v2, and v3, which should exist because the code is 2-dimensional. There are only two choices for each coefficient, 0 and 1, so there are only 8 linear combinations of v1, v2, and v3. All but one linear combination should be ruled out immediately, and that last one works.