Let W be the plane
3x + 2y − z = 0 in ℝ3.
Find a basis for W perpendicular
The Attempt at a Solution
I thought a basis for this plane could be generated just by letting x=0 and y=1, finding z and then doing the same thing but this time letting x=1 and y=0 and finding z. If you do that you get:
Apparently this is wrong, can anybody tell me what's wrong about this?