Let $X = \{(1,0,1), (1,1,0), (0,1,1)\}$ and $P$ is an orthogonal projection over $X$. Determine the representation matrix $P$ respect to the standard basis of Euclidean space $\mathbb{R} ^3$
I have trouble in the first step. Should I find every orthogonal projections of the vector in $X$ or what? I think it will lead to wrong computations later. Please help me.