设有向量组 $\boldsymbol{\alpha}_1=\left(\begin{array}{l}1 \\ 4 \\ 1 \\ 0\end{array}\right), \boldsymbol{\alpha}_2=\left(\begin{array}{r}2 \\ 1 \\ -1 \\ -3\end{array}\right), \boldsymbol{\alpha}_3=\left(\begin{array}{r}1 \\ 0 \\ -3 \\ -1\end{array}\right), \boldsymbol{\alpha}_4=\left(\begin{array}{r}0 \\ 2 \\ -6 \\ 3\end{array}\right)$, 求向量组的秩和一个最大无关组, 并把其余向量用该最大无关组线性表示.