设矩阵 $A=\left( \alpha _1, \alpha _2, \alpha _3, \alpha _4\right)$, 其中 $\alpha _1, \alpha _2, \alpha _3$ 线性无关, $\alpha _1+ \alpha _2+ \alpha _3+ \alpha _4= 0$, 向量 $b=\alpha_1-\alpha_2+\alpha_3-\alpha_4, c_1, c_2$ 表示任意常数, 则非齐次线性方程组 $A x=b$ 的通解为
$\text{A.}$ $c_1\left(\begin{array}{l}1 \\ 1 \\ 1 \\ 1\end{array}\right)+\left(\begin{array}{l}1 \\ -1 \\ 1 \\ -1\end{array}\right)$;
$\text{B.}$ $c_1\left(\begin{array}{l}1 \\ 1 \\ 1 \\ 1\end{array}\right)+c_2\left(\begin{array}{l}1 \\ -1 \\ 1 \\ -1\end{array}\right)$;
$\text{C.}$ $\left(\begin{array}{l}1 \\ 1 \\ 1 \\ 1\end{array}\right)+c_2\left(\begin{array}{c}1 \\ -1 \\ 1 \\ -1\end{array}\right)$;
$\text{D.}$ $c_1\left(\begin{array}{l}1 \\ 1 \\ 1 \\ 1\end{array}\right)-\left(\begin{array}{l}1 \\ -1 \\ 1 \\ -1\end{array}\right)$.