已知向量组 $\alpha_1, \alpha_2, \cdots, \alpha_s(s \geq 2)$ 线性无关，设
$$
\begin{aligned}
& \beta_1=\alpha_1+\alpha_2, \beta_2=\alpha_2+\alpha_3, \cdots, \\
& \beta_{s-1}=\alpha_{s-1}+\alpha_s, \beta_s=\alpha_s+\alpha_1
\end{aligned}
$$
讨论向量组 $\boldsymbol{\beta}_1, \boldsymbol{\beta}_2, \cdots, \boldsymbol{\beta}_s$ 的线性相关性.