设 $\alpha_1, \alpha_2, \alpha_3$ 是四元非齐次线形方程组 $A X=b$ 的三个解向量，且秩 $(A)=3$ ，
$$
\alpha_1=(1,2,3,4)^T, \alpha_2+\alpha_3=(0,1,2,3)^T \text {, }
$$
$c$ 表示任意常数，则线形方程组 $\boldsymbol{A} X=b$ 的通解 $\boldsymbol{X}=$
A. $\left(\begin{array}{l}1 \\ 2 \\ 3 \\ 4\end{array}\right)+c\left(\begin{array}{l}1 \\ 1 \\ 1 \\ 1\end{array}\right)$
B. $\left(\begin{array}{l}1 \\ 2 \\ 3 \\ 4\end{array}\right)+c\left(\begin{array}{l}0 \\ 1 \\ 2 \\ 3\end{array}\right)$
C. $\left(\begin{array}{l}1 \\ 2 \\ 3 \\ 4\end{array}\right)+c\left(\begin{array}{l}2 \\ 3 \\ 4 \\ 5\end{array}\right)$
D. $\left(\begin{array}{l}1 \\ 2 \\ 3 \\ 4\end{array}\right)+c\left(\begin{array}{l}3 \\ 4 \\ 5 \\ 6\end{array}\right)$