已知向量组: $\alpha_1=\left(\begin{array}{r}1 \\ -1 \\ 2 \\ 4\end{array}\right), \alpha_2=\left(\begin{array}{l}0 \\ 3 \\ 1 \\ 2\end{array}\right), \alpha_3=\left(\begin{array}{r}3 \\ 0 \\ 7 \\ 14\end{array}\right), \alpha_4=\left(\begin{array}{r}1 \\ -2 \\ 2 \\ 0\end{array}\right), \alpha_5=\left(\begin{array}{r}2 \\ 1 \\ 5 \\ 10\end{array}\right)$, 求该向量组的秩和一个最大无关组, 并把其余向量用最大无关组线性表示.