Let $A = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{pmatrix}$. If $u_1$ and $u_2$ are column matrices such that $Au_1 = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}$ and $Au_2 = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}$, then $u_1 + u_2$ is equal to

Question

( A ) $\begin{pmatrix} -1 \\ 1 \\ 0 \end{pmatrix}$
( B ) $\begin{pmatrix} -1 \\ 1 \\ -1 \end{pmatrix}$
( C ) $\begin{pmatrix} -1 \\ -1 \\ 0 \end{pmatrix}$
( D ) $\begin{pmatrix} 1 \\ -1 \\ -1 \end{pmatrix}$