设向量组 $\alpha_1, \alpha_2, \alpha_3$ 线性无关，向量组 $\beta_1, \beta_2, \beta_3$ 为

$$
\left\{\begin{array}{l}
\beta_1=2 \alpha_1+\alpha_2+\alpha_3 \\
\beta_2=-\alpha_1+3 \alpha_2+4 \alpha_3 \\
\beta_3=\alpha_1+\alpha_3
\end{array}\right.
$$


问 $\beta_1, \beta_2, \beta_3$ 是线性相关还是线性无关？并说明理由．