设 $\alpha_{1}=\left[\begin{array}{l}a_{1} \\ a_{2} \\ a_{3}\end{array}\right], \alpha_{2}=\left[\begin{array}{l}b_{1} \\ b_{2} \\ b_{3}\end{array}\right], \alpha_{3}=\left[\begin{array}{l}c_{1} \\ c_{2} \\ c_{3}\end{array}\right]$, 则三条直线
$$
\begin{aligned}
&a_{1} x+b_{1} y+c_{1}=0 \\
&a_{2} x+b_{2} y+c_{2}=0 \\
&a_{3} x+b_{3} y+c_{3}=0
\end{aligned}
$$
(其中 $\left(a_{i}^{2}+b_{i}^{2} \neq 0, i=1,2,3\right)$ 交于一点的充要条件是
A. $a_{1}, \alpha_{2}, \alpha_{3}$, 线性相关
B. $a_{1}, \alpha_{2}, \alpha_{3}$, 线性无关
C. 秩 $r\left(\alpha_{1}, \alpha_{2}, \alpha_{3}\right)=$ 秩 $r\left(\alpha_{1}, \alpha_{2}\right)$
D. $\alpha_{1}, \alpha_{2}, \alpha_{3}$ 线性相关, $\alpha_{1}, \alpha_{2}$ 线性无关