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.