设 $A$ 是 $n$ 阶矩阵，$\alpha$ 是 $n$ 维列向量，若 $R\left(\begin{array}{cc}A & \alpha \\ \alpha^T & 0\end{array}\right)=R(A)$ ，则线性方程组
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$\text{A.}$ $A X=\alpha$ 必有无穷多解
$\text{B.}$ $A X=\alpha$ 必有唯一解
$\text{C.}$ $\left(\begin{array}{cc}A & \alpha \\ \alpha^T & 0\end{array}\right)\binom{X}{y}=0$ 仅有零解
$\text{D.}$ $\left(\begin{array}{cc}A & \alpha \\ \alpha^T & 0\end{array}\right)\binom{X}{y}=0$ 必有非零解
$\text{E.}$
$\text{F.}$