设 $\alpha _1, \alpha _2, \alpha _3$ 是四元非齐次线性方程组 $A X = b$ 的三个解向量, 且 $r ( A )=3, \alpha _1=$ $(1,2,3,4)^{ T }, \alpha _2+ \alpha _3=(0,1,2,3)^{ T }, c$ 表任意常数, 则线性方程组 $A X = b$ 的通解 $X =$
$\text{A.}$ $\left(\begin{array}{l}1 \\ 2 \\ 3 \\ 4\end{array}\right)+c\left(\begin{array}{l}1 \\ 1 \\ 1 \\ 1\end{array}\right)$.
$\text{B.}$ $\left(\begin{array}{l}1 \\ 2 \\ 3 \\ 4\end{array}\right)+c\left(\begin{array}{l}0 \\ 1 \\ 2 \\ 3\end{array}\right)$.
$\text{C.}$ $\left(\begin{array}{l}1 \\ 2 \\ 3 \\ 4\end{array}\right)+c\left(\begin{array}{l}2 \\ 3 \\ 4 \\ 5\end{array}\right)$.
$\text{D.}$ $\left(\begin{array}{l}1 \\ 2 \\ 3 \\ 4\end{array}\right)+c\left(\begin{array}{l}3 \\ 4 \\ 5 \\ 6\end{array}\right)$.