设 $\boldsymbol{A}=\left(\begin{array}{ccc}1 & 3 & 9 \\ 2 & 0 & 6 \\ -3 & 1 & -7\end{array}\right), \boldsymbol{B}$ 为 3 阶非零矩阵, $\boldsymbol{\alpha}_1=\left(\begin{array}{c}0 \\ 1 \\ -1\end{array}\right), \boldsymbol{\alpha}_2=\left(\begin{array}{l}a \\ 2 \\ 1\end{array}\right), \boldsymbol{\alpha}_3=\left(\begin{array}{l}b \\ 1 \\ 0\end{array}\right)$ 为 $\boldsymbol{B} \boldsymbol{X}=\mathbf{0}$ 的解向量,且 $\boldsymbol{A X}=\boldsymbol{\alpha}_3$ 有解.
(I) 求常数 $a, b$;
(II) 求 $\boldsymbol{B X}=\mathbf{0}$ 的通解.