Nullspace Transpose[{{1,1,1,1,1,1},{1,1,-1,1,-1,-1},{1,1,-1,-1,1,1},{1,1,1,-1,-1,-1},{2,-2,0,0,0,0},{-8,0,0,0,0,0}}]

Uh oh! Wolfram|Alpha doesn't run without JavaScript.

Please enable JavaScript. If you don't know how, you can find instructionshere.Once you've done that, refresh this page to start using Wolfram|Alpha.