问题
已知，有线性方程组：$\left\{\begin{array}{l} a_{11} x_{1}+a_{12} x_{2}+\cdots+a_{1 n} x_{n}=b_{1} \\ a_{21} x_{1}+a_{22} x_{2}+\cdots+a_{2 n} x_{n}=b_{2} \\ \vdots \\ a_{n 1} x_{1}+a_{n 2} x_{2}+\cdots+a_{n n} x_{n}=b_{n} \end{array}\right.$
或者：
$\left\{\begin{array}{l} a_{11} x_{1}+a_{12} x_{2}+\cdots+a_{1 n} x_{n}=0 \\ a_{21} x_{1}+a_{22} x_{2}+\cdots+a_{2 n} x_{n}=0 \\ \vdots \\ a_{n 1} x_{1}+a_{n 2} x_{2}+\cdots+a_{n n} x_{n}=0 \end{array}\right.$
则，上述线性方程组的系数行列式 $D$ $=$ $?$
选项
[A]. $D$ $=$ $\left|\begin{array}{ccc} a_{11} & \cdots & a_{(1) (n-1)} & b_{1} \\ \vdots & & \vdots & \vdots \\ a_{n 1} & \cdots & a_{(n-1) (n-1)} & b_{n} \end{array}\right|$[B]. $D$ $=$ $\left|\begin{array}{ccc} a_{n1} & \cdots & a_{n n} \\ \vdots & & \vdots \\ a_{1 1} & \cdots & a_{1 n} \end{array}\right|$
[C]. $D$ $=$ $\left|\begin{array}{ccc} a_{11} & \cdots & a_{1 n} \\ \vdots & & \vdots \\ a_{n 1} & \cdots & a_{n n} \end{array}\right|$
[D]. $D$ $=$ $\left|\begin{array}{ccc} b_{1} & a_{12} & \cdots & a_{1 n} \\ \vdots & \vdots & & \vdots \\b_{n} & a_{n 2} & \cdots & a_{n n} \end{array}\right|$
$D$ $=$ $\left|\begin{array}{ccc} a_{11} & \cdots & a_{1 n} \\ \vdots & & \vdots \\ a_{n 1} & \cdots & a_{n n} \end{array}\right|$