Let P is set all vectors $(x\_1,x\_2,x\_3,x\_4) \in R^{4}$ for which $x\_1 + x\_2 + x\_3 + x\_4=0$

a) Find one base of subspace $P^{\bot}$

b) Prove that P is subspace of $R^{4}$ then construct matrices which P is null space.

a) I found base $(1,1,1,1)$ that is easy
b) I know how to prove that $P$ is subspace, but I do not know if my matrix is good, because what means that P is null space, does that mean that for every vector $x\in P$ $Ax=0$. So matrices $A$ are

> 
> A=$\begin{bmatrix}
>  1& 1& 1& 1\\
>  1& 1& 1& 1\\
>  1 & 1& 1& 1\\
>  1 & 1& 1& 1
>  \end{bmatrix}$.
> 
> 
>