## 问题

$\left\{\begin{array}{l} a_{11} x_{1}+a_{12} x_{2}+\cdots+a_{1 n} x_{n}=0 \\ a_{21} x_{1}+a_{22} x_{2}+\cdots+a_{2 n} x_{n}=0 \\ \vdots \\ a_{n 1} x_{1}+a_{n 2} x_{2}+\cdots+a_{n n} x_{n}=0 \end{array}\right.$.

## 选项

[A].   $D$ $=$ $1$

[B].   $D$ $\neq$ $1$

[C].   $D$ $=$ $0$

[D].   $D$ $\neq$ $0$

$x_{1}$ $=$ $x_{2}$ $=$ $\cdots$ $=$ $x_{n}$ $=$ $0$.

## 问题

$\left\{\begin{array}{l} a_{11} x_{1}+a_{12} x_{2}+\cdots+a_{1 n} x_{n}=b_{1} \\ a_{21} x_{1}+a_{22} x_{2}+\cdots+a_{2 n} x_{n}=b_{2} \\ \vdots \\ a_{n 1} x_{1}+a_{n 2} x_{2}+\cdots+a_{n n} x_{n}=b_{n} \end{array}\right.$

## 选项

[A].   $x_{1}$ $=$ $D_{1}$, $x_{2}$ $=$ $D_{2}$, $\cdots$, $x_{n}$ $=$ $D_{n}$

[B].   $x_{1}$ $=$ $D_{1} D$, $x_{2}$ $=$ $D_{2} D$, $\cdots$, $x_{n}$ $=$ $D_{n} D$

[C].   $x_{1}$ $=$ $\frac{D_{1}}{D}$, $x_{2}$ $=$ $\frac{D_{2}}{D}$, $\cdots$, $x_{n}$ $=$ $\frac{D_{n}}{D}$

[D].   $x_{1}$ $=$ $\frac{D}{D_{1}}$, $x_{2}$ $=$ $\frac{D}{D_{2}}$, $\cdots$, $x_{n}$ $=$ $\frac{D}{D_{n}}$

$x_{1}$ $=$ $\frac{\textcolor{orange}{D_{1}}}{\textcolor{cyan}{D}}$, $x_{2}$ $=$ $\frac{\textcolor{orange}{D_{2}}}{\textcolor{cyan}{D}}$, $\cdots$, $x_{n}$ $=$ $\frac{\textcolor{orange}{D_{n}}}{\textcolor{cyan}{D}}$

## 问题

$\left\{\begin{array}{l} a_{11} x_{1}+a_{12} x_{2}+\cdots+a_{1 n} x_{n}=b_{1} \\ a_{21} x_{1}+a_{22} x_{2}+\cdots+a_{2 n} x_{n}=b_{2} \\ \vdots \\ a_{n 1} x_{1}+a_{n 2} x_{2}+\cdots+a_{n n} x_{n}=b_{n} \end{array}\right.$

$D$ $=$ $\left|\begin{array}{ccc} a_{11} & \cdots & a_{1 n} \\ \vdots & & \vdots \\ a_{n 1} & \cdots & a_{n n} \end{array}\right|$

## 选项

[A].   $D$ $=$ $1$

[B].   $D$ $\neq$ $1$

[C].   $D$ $=$ $0$

[D].   $D$ $\neq$ $0$

$D$ $\neq$ $0$

## 问题

$\left\{\begin{array}{l} a_{11} x_{1}+a_{12} x_{2}+\cdots+a_{1 n} x_{n}=b_{1} \\ a_{21} x_{1}+a_{22} x_{2}+\cdots+a_{2 n} x_{n}=b_{2} \\ \vdots \\ a_{n 1} x_{1}+a_{n 2} x_{2}+\cdots+a_{n n} x_{n}=b_{n} \end{array}\right.$

$\left\{\begin{array}{l} a_{11} x_{1}+a_{12} x_{2}+\cdots+a_{1 n} x_{n}=0 \\ a_{21} x_{1}+a_{22} x_{2}+\cdots+a_{2 n} x_{n}=0 \\ \vdots \\ a_{n 1} x_{1}+a_{n 2} x_{2}+\cdots+a_{n n} x_{n}=0 \end{array}\right.$

## 选项

[A].   $D$ $=$ $\left|\begin{array}{ccc} b_{1} & a_{12} & \cdots & a_{1 n} \\ \vdots & \vdots & & \vdots \\b_{n} & a_{n 2} & \cdots & a_{n n} \end{array}\right|$

[B].   $D$ $=$ $\left|\begin{array}{ccc} a_{11} & \cdots & a_{(1) (n-1)} & b_{1} \\ \vdots & & \vdots & \vdots \\ a_{n 1} & \cdots & a_{(n-1) (n-1)} & b_{n} \end{array}\right|$

[C].   $D$ $=$ $\left|\begin{array}{ccc} a_{n1} & \cdots & a_{n n} \\ \vdots & & \vdots \\ a_{1 1} & \cdots & a_{1 n} \end{array}\right|$

[D].   $D$ $=$ $\left|\begin{array}{ccc} a_{11} & \cdots & a_{1 n} \\ \vdots & & \vdots \\ a_{n 1} & \cdots & a_{n n} \end{array}\right|$

$D$ $=$ $\left|\begin{array}{ccc} a_{11} & \cdots & a_{1 n} \\ \vdots & & \vdots \\ a_{n 1} & \cdots & a_{n n} \end{array}\right|$