We consider the three vectors
$$w_1 = \begin{pmatrix}0\\1\\0\end{pmatrix}, \quad w_2 = \begin{pmatrix}1\\-1\\0\end{pmatrix}, \quad w_3 = \begin{pmatrix}-1\\0\\-1\end{pmatrix}.$$
Verify that $s_{w_1}$, $s_{w_2}$ and $s_{w_3}$ belong to $\Gamma$ and calculate the corresponding matrices.