Let V be the 2-dim subspace of R^3 spanned by V1 = (1,1,1) and V2 = (-2,0,1). Find the orthogonal compliment Vperpendicular.
2. Relevant equation
X + Y + Z = 0
-5X + Y + 4Z = 0
The Attempt at a Solution
Firstly, I orthogonalize the basis for V and get the vectors (1,1,1) and (-5,1,4).
Then I apply the dot product and end up with the above equations. I found that the solution space for this system of equations is a single vector (x,y,z) = (.5z, -1.5z,z) . Usually I will get 2 vectors and then orthogonalize them as the basis for the orthogonal compliment. Can this single vector (.5,-1.5,1) be the orhogonal compliment? Or did I make a mistake somewhere? Please help.