已知向量组 $\alpha_1=\left[\begin{array}{c}1 \\ 1 \\ 1 \\ -1\end{array}\right], \alpha_2=\left[\begin{array}{l}1 \\ 2 \\ 1 \\ 1\end{array}\right], \alpha_3=\left[\begin{array}{c}3 \\ 4 \\ 3 \\ -1\end{array}\right], \alpha_4=\left[\begin{array}{l}2 \\ 2 \\ 2 \\ 1\end{array}\right]$, 求向量组 $\alpha_1, \alpha_2, \alpha_3, \alpha_4$ 的一个 极大无关组，并把其余向量用此极大无关组表示出来