已知向量组 $\alpha_1=\left(\begin{array}{c}1 \\ 2 \\ -3\end{array}\right), \alpha_2=\left(\begin{array}{l}3 \\ 0 \\ 1\end{array}\right), \alpha_3=\left(\begin{array}{c}9 \\ 6 \\ -7\end{array}\right)$ 和
$\beta_1=\left(\begin{array}{c}0 \\ 1 \\ -1\end{array}\right), \beta_2=\left(\begin{array}{l}a \\ 2 \\ 1\end{array}\right), \beta_3=\left(\begin{array}{l}b \\ 1 \\ 0\end{array}\right) ;$ 已知 $\beta_3$ 可以由 $\alpha_1, \alpha_2, \alpha_3$ 线性表示，且 $\alpha_1, \alpha_2, \alpha_3$
与 $\beta_1, \beta_2, \beta_3$ 具有相同的秩，求 $a, b$ 的值。