线性方程组中的系数行列式（C006）

问题

已知，有线性方程组：

{\begin{cases} a_{11} x_{1} + a_{12} x_{2} + \dots + a_{1 n} x_{n} = b_{1} \\ a_{21} x_{1} + a_{22} x_{2} + \dots + a_{2 n} x_{n} = b_{2} \\ ⋮ \\ a_{n 1} x_{1} + a_{n 2} x_{2} + \dots + a_{n n} x_{n} = b_{n} \end{cases}

或者：
${\begin{cases} a_{11} x_{1} + a_{12} x_{2} + \dots + a_{1 n} x_{n} = 0 \\ a_{21} x_{1} + a_{22} x_{2} + \dots + a_{2 n} x_{n} = 0 \\ ⋮ \\ a_{n 1} x_{1} + a_{n 2} x_{2} + \dots + a_{n n} x_{n} = 0 \end{cases}$

则，上述线性方程组的系数行列式 $D$ $=$ $?$

选项

[A].

D

=

| \begin{array}{ccc} a_{11} & \dots & a_{(1) (n - 1)} & b_{1} \\ ⋮ & ⋮ & ⋮ \\ a_{n 1} & \dots & a_{(n - 1) (n - 1)} & b_{n} \end{array} |

[B].

D

=

| \begin{array}{ccc} a_{n 1} & \dots & a_{n n} \\ ⋮ & ⋮ \\ a_{11} & \dots & a_{1 n} \end{array} |

[C].

D

=

| \begin{array}{ccc} a_{11} & \dots & a_{1 n} \\ ⋮ & ⋮ \\ a_{n 1} & \dots & a_{n n} \end{array} |

[D].

D

=

| \begin{array}{ccc} b_{1} & a_{12} & \dots & a_{1 n} \\ ⋮ & ⋮ & ⋮ \\ b_{n} & a_{n 2} & \dots & a_{n n} \end{array} |

答案

$D$ $=$ $| \begin{array}{ccc} a_{11} & \dots & a_{1 n} \\ ⋮ & ⋮ \\ a_{n 1} & \dots & a_{n n} \end{array} |$

问题

选项

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