Let $S$ be the subspace of $\mathbb{R}^4$ spanned by $x_1=(1,0,-2,1)^T$ and $x_2=(0,1,3,-2)^T$. Find a basis for $S_\perp$.
For this kind of question, if the subspace is spanned by one vector, I know how to deal with it by setting a vector $Y=(y_1,y_2,y_3)$ such that $x^Ty=0$.
But for this question, the subspace is spanned by two vectors, I don't know how to do it. I guess maybe I should multiply the two vectors and then set $y=(y_1,y_2,y_3)$ and
then calculate $x^Ty=0$ ?