贺胖娇的编程之旅......

行列式

2022.06.20

二阶行列式

1 例如以下二元线性方程组

$$\begin{cases} a_{11}x_1+a_{12}x_2=b_1\\ a_{21}x_1+a_{22}x_2=b_2\\ \end{cases} $$

2 使用消元法可以得到上式中x_1和x_2的解

$$\x_1=(b_1a_{22}-a_{12}b_2)/(a_{11}a_{22}-a_{12}a_{21})$$
$$\x_2=(b_2a_{11}-a_{21}b_1)/(a_{11}a_{22}-a_{12}a_{21})$$

3 $$ \left| \begin{array}{cccc} 1 & 0 & 0 \
-5 & 2 & 3\
3 & 3 & 5 \end{array} \right| $$

2

$ \left[ \begin{array}{cccc} 1 & 2 & \cdots & 4 \
7 & 6 &{\cdot^{\cdot^{\cdot}}} & 5 \
\vdots & \vdots & \ddots & \vdots \
8 & 9 & \cdots & 0 \
\end{array} \right] $

3

$$
\left|
\begin{array}{cccc}
1  &  0   & 0 \\
-5  &  2   & 3\\
3  &  3   & 5
\end{array}
\right|
$$

4
$\sum_{i=0}^N\int_{a}^{b}g(t,i)\text{d}t$

5
$$\sum_{i=0}N\int_{a}{b}g(t,i)\text{d}t$$

6
$$\begin{cases} a_1x+b_1y+c_1z=d_1\
a_2x+b_2y+c_2z=d_2\
a_3x+b_3y+c_3z=d_3\
\end{cases} $$

7
3^4

8

$$ \left| \begin{array}{cccc} 1 & 0 & 0 \\ -5 & 2 & 3\\ 3 & 3 & 5 \end{array} \right| $$

9
$\sum_{i=0}^N\int_{a}^{b}g(t,i)\text{d}t$

10 asdasd\( $$\sum_{i=0}N\int_{a}{b}g(t,i)\text{d}t$$ \)aaa

1000 4347 =5347 -700 4600 -1000 1500 * 5 = 11722*5=58610

-20000 -20000 -10000

1 2 -> 1 2 3 2 3 -> 1 2 3 1 -> 1 2 2 ->

|情况|key| |没有置顶数据|1| |有一条置顶数据|2| |有两条置顶数据|3| |有三条置顶数据|报错|

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