# Math Help - Basis

1. ## Basis

U = span{(1 1 0), (0 1 1)}
Find a basis for U(prep)

2. Originally Posted by ishan
U = span{(1 1 0), (0 1 1)}. Find a basis for U(prep)
$(x,y,z) \in U^{\perp}$ if and only if $(x,y,z) \cdot (1,1,0)=(x,y,z) \cdot (0,1,1)=0.$ that will give you: $x+y=y+z=0.$ thus: $x=z=-y$ and $y$ can be anything. so $\{(-1,1,-1) \}$ is a beasis for $U^{\perp}. \ \Box$