finding basis of a set given span I am given $W=\operatorname{span}\left(\{\begin{pmatrix}
x\\y\\z\\w\end{pmatrix}\}| x+y=0\right)$.

To find a basis for this set, I need to find a linearly independent set of vectors such that $a_1v_1+a_1v_2+\ldots+a_nv_n=0\implies a_i=0\forall i$

I am having some trouble finding such a basis. Can anyone point me in the correct direction.
Hint:

How can you describe the set of solutions of this linear equation? How many parameters do you need? Can you say what its dimension is?
Write the sum in terms of the constraint. 

(x, y, z, w) = (-y, y, z, w) = y(-1, 1, 0, 0) + z(0, 0, 1, 0) + w(0, 0, 0, 1). 

Note that the vectors after the equal sign are L.I. and generate the set. Thus, they form a basis by the Replacement Theorem.