已知向量组 $\alpha_1=\left[\begin{array}{lll}1 & 1 & 1\end{array}\right]^{ T }, \alpha_2=\left[\begin{array}{lll}-1 & 0 & 1\end{array}\right]^{ T }, \alpha_3=\left[\begin{array}{lll}0 & 1 & 2\end{array}\right]^{ T }$ ， $\alpha_4=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]^{ T }$ ，求此向量组的秩和一个极大无关组，并将其余向量用此极大无关组线性表示．