Given the subspace $L=\{(a,b,c)\in \mathbb{R}^3 : 2a-4b-c=0 \}$ I need to find the projection of a vector onto this subspace. I therefore need to find the span of this subspace/plane. How do I do that?
Edit: the span of a subspace is probably not what I am looking for. What I believe I actually wanted to ask is what a basis of this subspace is such than $span=\{ \vec{V_1}, \vec{V_2}... \}$ spans the subspace $L$ and $V_1$ and $V_2$... is a basis for $L$
$L$ has codimension $1$, as it is given by one linear equation (hyperplane) and so dimension $2$. A basis is e.g. $\{(2,1,0), (0,1,-4)\}$.