Answer
$u_1 + v_1 + w_1=0$
$u_2 + v_2 + w_2=0$
$u_3 + v_3 + w_3=0$
Any matrix A whose elements satisfy the 3 equation above is a solution to this problem.
Work Step by Step
$\begin{bmatrix}
u_1 & v_1 & w_1\\
u_2 & v_2 & w_2\\
u_3 & v_3 & w_3\\
\end{bmatrix}\begin{bmatrix}
1\\
1\\
1\\
\end{bmatrix}
$
$u_1 + v_1 + w_1=0$
$u_2 + v_2 + w_2=0$
$u_3 + v_3 + w_3=0$
Any matrix A whose elements satisfy the 3 equation above is a solution to this problem.
One example is:
$\begin{bmatrix}
2 & -1 & -1\\
4 & 2 & -6\\
-4 & -4 & 8\\
\end{bmatrix}$~$\begin{bmatrix}
1 & 0 & -1\\
0 & 1 & -1\\
0 & 0 & 0\\
\end{bmatrix}$
