已知向量组 $\alpha_1=\left[\begin{array}{llll}1 & 2 & 1 & 0\end{array}\right]^{ T }, \alpha_2=\left[\begin{array}{llll}1 & 3 & 2 & -1\end{array}\right]^{ T }$ ， $\alpha_3=\left[\begin{array}{llll}1 & a & 0 & 1 \end{array}\right]^{T}$, $ \alpha_4=\left[\begin{array}{llll} 2 & 7 & 3 & a-2\end{array}\right]^{T}$ $\beta=\left[\begin{array}{llll}3 & 8 & 4 & b-1\end{array}\right]^{ T }$ ，讨论 $a, b$ 为何值时 $\beta$ 可由向量组 $\alpha_1, \alpha_2, \alpha_3, \alpha_4$ 唯一线性表示；能线性表示但不唯一；不能线性表示．