设有向量组 $\alpha_1=\left(\begin{array}{l}1 \\ 3 \\ 2 \\ 0\end{array}\right), \alpha_2=\left(\begin{array}{c}7 \\ 0 \\ 14 \\ 3\end{array}\right), \quad \alpha_3=\left(\begin{array}{c}2 \\ -1 \\ 0 \\ 1\end{array}\right), \quad \alpha_4=\left(\begin{array}{l}5 \\ 1 \\ 6 \\ 2\end{array}\right)$,
(1) 求该向量组的秩;
(2) 求该向量组的一个极大无关组, 并把其余向量分别用求得的极大无关组线性表出.