Let S be the subspace of R^3 spanned by x=(1,-1,1)^T. Find a basis for the orthogonal complement of S. I don't even know where to start... I would appreciate your help!
If (a,b,c)^T is a general vector in R^3 then it's orthogonal to (1,-1,1)^T if the dot product is zero. What conditions does that give you on a, b and c?