$\alpha_1=\left(\begin{array}{r}2 \\ 2 \\ -1\end{array}\right), \alpha_2=\left(\begin{array}{l}0 \\ 4 \\ 8\end{array}\right), \alpha_3=\left(\begin{array}{r}-1 \\ a \\ 3\end{array}\right), \beta=\left(\begin{array}{l}1 \\ 1 \\ 2\end{array}\right), \beta$ 不能由 $\alpha_1, \alpha_2, \alpha_3$ 线性表示, 求 $a$ 的值.