Find the basis of the null space for the matrix
$$D = \begin{bmatrix}0 & 0 & 0 & 0\\0 & 1 & 1 & 0\\1 & 1 & 0 & 0\\1 &1 & 0 & 0\end{bmatrix}.$$
I computed the solution by letting eigenvectors $(x,y,z,w)$ such that $y+z=0,x+y=0$, and I got a basis vector $\{(1,-1,1,0), (0,0,0,1)\}$ . But from one textbook I have found the solution as $\{(1,0,0,0),(0,0,1,1)\}$. May I made a mistake? Thanks!