1. ## Basis Problem

I do not understand how to solve this problem:
Let W = {(s+4t,t,s,2s-t)| s,t are elements are reals}. Where W is a subspace of R^4.

Find the basis for W.

I understand that a basis means that W spans R^4 and is linearly independent. But I fail to understand how to complete this problem. I think I am missing something small.

Any help would be appreciated.

2. you can see that,
$w=\left \{ s(1,0,1,2)+t(4,1,0,-1)\mid s,t\in \mathbb{R} \right \}=\texttt{Span}((1,0,1,2),(4,1,0,-1))$
which means $((1,0,1,2),(4,1,0,-1))$ is a Basis of $\mathbb{W}$.