设 $A=\left(\alpha_1, \alpha_2, \alpha_3, \alpha_4\right)$ 为 4 阶正交矩阵。若矩阵 $B=\left(\begin{array}{l}\alpha_1^T \\ \alpha_2^T \\ \alpha_3^T\end{array}\right), \beta=\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right), k$ 表示任意常数, 则线性方程组 $B x=\beta$ 的通解 $x=(\quad)$
A
$\alpha_2+\alpha_3+\alpha_4+k \alpha_1$;
B
$\alpha_1+\alpha_3+\alpha_4+k \alpha_2$;
C
$\alpha_1+\alpha_2+\alpha_4+k \alpha_3$;
D
$\alpha_1+\alpha_2+\alpha_3+k \alpha_4$ 。
E
F