Find a basis from cartesian equations

[Tonig00]

Thanks very much for your helpful answers.
Both works:
First give {[-2*a-b+2*c,a,-b-3*c,b,c]}which giving values to a,b,c give same answer in one step (before three).

Second just jumps one step, so both together make it easier.

Anyway, if someone finds a direct way tell me
thanks again

Toni