For any value of \(\alpha\), \(x_1=-\alpha-4\), \(x_2=-3+\alpha\), and \(x_3=\alpha\) are a solution of the associated system of equations. Or we can write the solutions as
\[\mathbf{x}=\alpha
\begin{pmatrix}
-1\\
1\\
1\\
\end{pmatrix}
+
\begin{pmatrix}
-4\\
-3\\
0
\end{pmatrix}
\]
for any value of \(\alpha\).