fix latex

Author: Dilettante258

Task2/index.md

@@ -43,7 +43,7 @@ a\\b: a右除b，即矩阵方程Xa=b的解
 
 用矩阵除法解下列线性方程组，判断解的意义，并用矩阵乘法验算:
 
-\(1\) $\begin{pmatrix}4 & 1 & - 1 \\\3 & 2 & - 6 \\\1 & - 5 & 3\end{pmatrix}\begin{pmatrix}x_{1} \\\x_{2} \\\x_{3}\end{pmatrix} = \begin{pmatrix}9 \\\ - 2 \\\1\end{pmatrix}$
+\(1\) $\begin{pmatrix}4 & 1 & - 1 \\\ 3 & 2 & - 6 \\\1 & - 5 & 3\end{pmatrix}\begin{pmatrix}x_{1} \\\x_{2} \\\x_{3}\end{pmatrix} = \begin{pmatrix}9 \\\ - 2 \\\1\end{pmatrix}$
 
 定义函数：
 
@@ -131,18 +131,7 @@ A*x
 >
 > ​	1
 
-\(3\) $\begin{pmatrix}
-4 & 1 \\\
-3 & 2 \\\
-1 & - 5
-\end{pmatrix}\begin{pmatrix}
-x_{1} \\\
-x_{2}
-\end{pmatrix} = \begin{pmatrix}
-1 \\\
-1 \\\
-1
-\end{pmatrix}$;
+\(3\) $\begin{pmatrix} 4 & 1 \\\ 3 & 2 \\\ 1 & - 5 \end{pmatrix}\begin{pmatrix} x_{1} \\\ x_{2} \end{pmatrix} =  \begin{pmatrix} 1 \\\ 1 \\\ 1 \end{pmatrix}$;
 
 代码：
 
@@ -172,22 +161,7 @@ A*x
 >
 > 0.9404
 
-\(4\) $\begin{pmatrix}\begin{matrix}2 & 1 \\\1 & 2 \\\1 & 1\end{matrix} & \begin{matrix}1 & 1 \\\
-1 & - 1 \\\
-2 & 1
-\end{matrix}
-\end{pmatrix}\left( \begin{array}{r}
-\begin{matrix}
-x_{1} \\\
-x_{2} \\\
-x_{3}
-\end{matrix} \\\
-x_{4}
-\end{array} \right) = \begin{pmatrix}
-1 \\\
-2 \\\
-3
-\end{pmatrix}$;
+\(4\) $\begin{pmatrix}\begin{matrix}2 & 1 \\\1 & 2 \\\1 & 1\end{matrix} & \begin{matrix}1 & 1 \\\ 1 & - 1 \\\ 2 & 1 \end{matrix} \end{pmatrix}\left( \begin{array}{r} \begin{matrix} x_{1} \\\ x_{2} \\\ x_{3} \end{matrix} \\\ x_{4} \end{array} \right) = \begin{pmatrix} 1 \\\ 2 \\\ 3 \end{pmatrix}$;
 
 代码：
 
@@ -225,35 +199,11 @@ A*x
 
  求下列矩阵的行列式、逆、特征值和特征向量；
 
-(1) $\begin{pmatrix}
-4 & 1 & - 1 \\\
-3 & 2 & - 6 \\\
-1 & - 5 & 3
-\end{pmatrix}$
-
-(2) $\begin{pmatrix}1 & 1 & - 1 \\\0 & 2 & - 1 \\\- 1 & 2 & 0\end{pmatrix}$
-
-(3) $\begin{pmatrix}
-\begin{matrix}
-\begin{matrix}
-5 & 7 \\\
-7 & 10
-\end{matrix} \\\
-\begin{matrix}
-6 & 8 \\\
-5 & 7
-\end{matrix}
-\end{matrix} & \begin{matrix}
-\begin{matrix}
-6 & 5 \\\
-8 & 7
-\end{matrix} \\\
-\begin{matrix}
-10 & 9 \\\
-9 & 10
-\end{matrix}
-\end{matrix}
-\end{pmatrix}$
+(1) $\begin{pmatrix} 4 & 1 & - 1 \\\ 3 & 2 & - 6 \\\ 1 & - 5 & 3 \end{pmatrix}$
+
+(2) $\begin{pmatrix}1 & 1 & - 1 \\\ 0 & 2 & - 1 \\\ - 1 & 2 & 0\end{pmatrix}$
+ 
+(3) $\begin{pmatrix}5&7&6&5\\\ 7&10&8&7\\\ 6&8&10&9\\\ 5&7&9&10\end{pmatrix}$
 
 (1)代码：
 
@@ -296,27 +246,27 @@ matrixProperties(A)
 >
 > 逆矩阵为:
 >
->   0.2553  -0.0213  0.0426
+> ​	 0.2553  -0.0213  0.0426
 >
->   0.1596  -0.1383  -0.2234
+> ​	 0.1596  -0.1383  -0.2234
 >
->   0.1809  -0.2234  -0.0532
+> ​	 0.1809  -0.2234  -0.0532
 >
 > 特征值为:
 >
->   -3.0527
+> ​	 -3.0527
 >
->   3.6760
+> ​	 3.6760
 >
->   8.3766
+> ​	 8.3766
 >
 > 特征向量为:
 >
->   0.0185  -0.9009  -0.3066
+> ​	 0.0185  -0.9009  -0.3066
 >
->   -0.7693  -0.1240  -0.7248
+> ​	 -0.7693  -0.1240  -0.7248
 >
->   -0.6386  -0.4158  0.6170
+> ​	 -0.6386  -0.4158  0.6170
 
 (2)代码：
 
@@ -331,27 +281,27 @@ matrixProperties(A)
 >
 > 逆矩阵为:
 >
->   2.0000  -2.0000  1.0000
+> ​	 2.0000  -2.0000  1.0000
 >
->   1.0000  -1.0000  1.0000
+> ​	 1.0000  -1.0000  1.0000
 >
->   2.0000  -3.0000  2.0000
+> ​	 2.0000  -3.0000  2.0000
 >
 > 特征值为:
 >
->   1.0000 + 0.0000i
+> ​	 1.0000 + 0.0000i
 >
->   1.0000 + 0.0000i
+> ​	 1.0000 + 0.0000i
 >
->   1.0000 - 0.0000i
+> ​	 1.0000 - 0.0000i
 >
 > 特征向量为:
 >
->   0.5774 + 0.0000i  0.5773 + 0.0000i  0.5773 - 0.0000i
+> ​	 0.5774 + 0.0000i  0.5773 + 0.0000i  0.5773 - 0.0000i
 >
->   0.5774 + 0.0000i  0.5773 + 0.0000i  0.5773 - 0.0000i
+> ​	 0.5774 + 0.0000i  0.5773 + 0.0000i  0.5773 - 0.0000i
 >
->   0.5773 + 0.0000i  0.5774 + 0.0000i  0.5774 + 0.0000i
+> ​	 0.5773 + 0.0000i  0.5774 + 0.0000i  0.5774 + 0.0000i
 
 (3)代码：
 
@@ -364,33 +314,33 @@ matrixProperties(A)
 >
 > 逆矩阵为:
 >
->   68.0000 -41.0000 -17.0000  10.0000
+> ​	 68.0000 -41.0000 -17.0000  10.0000
 >
 >  -41.0000  25.0000  10.0000  -6.0000
 >
 >  -17.0000  10.0000  5.0000  -3.0000
 >
->   10.0000  -6.0000  -3.0000  2.0000
+> ​	 10.0000  -6.0000  -3.0000  2.0000
 >
 > 特征值为:
 >
->   0.0102
+> ​	 0.0102
 >
->   0.8431
+> ​	 0.8431
 >
->   3.8581
+> ​	 3.8581
 >
->   30.2887
+> ​	 30.2887
 >
 > 特征向量为:
 >
->   0.8304  0.0933  0.3963  0.3803
+> ​	 0.8304  0.0933  0.3963  0.3803
 >
->   -0.5016  -0.3017  0.6149  0.5286
+> ​	 -0.5016  -0.3017  0.6149  0.5286
 >
->   -0.2086  0.7603  -0.2716  0.5520
+> ​	 -0.2086  0.7603  -0.2716  0.5520
 >
->   0.1237  -0.5676  -0.6254  0.5209
+> ​	 0.1237  -0.5676  -0.6254  0.5209
 
 ## 4(课本习题7)
 
@@ -438,19 +388,19 @@ diagonalizeMatrix(A)
 >
 > 对角矩阵为:
 >
->   -3.0527     0     0
+> ​	 -3.0527     0     0
 >
 > ​     0  3.6760     0
 >
 > ​     0     0  8.3766
 >
 > 相似变换矩阵为:
 >
->   0.0185  -0.9009  -0.3066
+> ​	 0.0185  -0.9009  -0.3066
 >
->   -0.7693  -0.1240  -0.7248
+> ​	 -0.7693  -0.1240  -0.7248
 >
->   -0.6386  -0.4158  0.6170
+> ​	 -0.6386  -0.4158  0.6170
 
 (2)代码：
 
@@ -478,7 +428,7 @@ diagonalizeMatrix(A)
 >
 > 对角矩阵为:
 >
->   0.0102     0     0     0
+> ​	 0.0102     0     0     0
 >
 > ​     0  0.8431     0     0
 >
@@ -488,13 +438,13 @@ diagonalizeMatrix(A)
 >
 > 相似变换矩阵为:
 >
->   0.8304  0.0933  0.3963  0.3803
+> ​	 0.8304  0.0933  0.3963  0.3803
 >
->   -0.5016  -0.3017  0.6149  0.5286
+> ​	 -0.5016  -0.3017  0.6149  0.5286
 >
->   -0.2086  0.7603  -0.2716  0.5520
+> ​	 -0.2086  0.7603  -0.2716  0.5520
 >
->   0.1237  -0.5676  -0.6254  0.5209
+> ​	 0.1237  -0.5676  -0.6254  0.5209
 
 ## 5(课本习题9)
 
@@ -556,13 +506,13 @@ vectorProperties(A);
 >
 > 最大线性无关组为:
 >
->    4   2   3
+> ​	  4   2   3
 >
->   -3  -1  -2
+> ​	 -3  -1  -2
 >
->    1   3   3
+> ​	  1   3   3
 >
->    3   5   4
+> ​	  3   5   4
 >
 > a3用该最大无关组线性表示为
 >
@@ -589,23 +539,23 @@ A = [1 -2 2;-2 -2 4;2 4 -2]
 
 > A = 3×3  
 >
->    1  -2   2
+> ​	  1  -2   2
 >
->   -2  -2   4
+> ​	 -2  -2   4
 >
->    2   4  -2
+> ​	  2   4  -2
 >
 > Q = 3×3  
 >
->   0.3333  0.8944  -0.2981
+> ​	 0.3333  0.8944  -0.2981
 >
->   0.6667  -0.4472  -0.5963
+> ​	 0.6667  -0.4472  -0.5963
 >
->   -0.6667     0  -0.7454
+> ​	 -0.6667     0  -0.7454
 >
 > D = 3×3  
 >
->   -7.0000     0     0
+> ​	 -7.0000     0     0
 >
 > ​     0  2.0000     0
 >

Task3/index.md

@@ -442,7 +442,7 @@ title('马鞍面'); % 给图形添加标题
 ```
 
 输出：
-<div class="image-container">
+<div class="image-container" id="fitPhone">
     <img src="https://pic.wang1m.tech/uploads/2404/661e4b9d8b015.png" alt="image-20240416175749315" style="zoom: 67%;" />
     <img src="https://pic.wang1m.tech/uploads/2404/661e4ba7702fc.png" alt="image-20240416175759049" style="zoom: 67%;" />
 </div>

Task4/index.md

@@ -23,10 +23,7 @@ factor(f)
 
 ## 2(课本习题3)
 
-求矩阵$A = \begin{pmatrix}
-1 & 2 \\\
-2 & a
-\end{pmatrix}$的逆和特征值.
+求矩阵$A = \begin{pmatrix}1 & 2 \\\ 2 & a \end{pmatrix}$的逆和特征值.
 
 代码：
 
@@ -46,9 +43,9 @@ e = eig(A)
 
 计算极限
 
-$
+$$
 \lim_{x \rightarrow \infty}\left( 3^{x} + 9^{x} \right)^{\frac{1}{x}},\lim_{y \rightarrow 0^{+}}{\lim_{x \rightarrow 0^{+}}\frac{\ln{(2x + e^{- y})}}{\sqrt{x^{3} + y^{2}}}}，\\\ \lim_{x \rightarrow \infty}\frac{\ln{(1 + \frac{1}{x})}}{arccot \, x},\lim_{x \rightarrow 0}\frac{1 - \sqrt{1 - x^{2}}}{e^{x} - \cos x}
-$
+$$
 
 代码：
 
@@ -119,7 +116,8 @@ s=subs(s,{x,y,z},{1,1,3})
 
 (Taylor展开)求下列函数在$x = 0$的Taylor幂级数展开式(n=8):
 
-$$e^{x},\ \ \ln{(1 + x)},\ \ \sin x,\ \ \ln{(x + \sqrt{1 + x^{2}})},\ \ \frac{1}{x^{2} - 3x + 2}.$$
+$$e^{x}, \ln{(1 + x)}, \sin x,$$
+$$\ln{(x + \sqrt{1 + x^{2}})}, \frac{1}{x^{2} - 3x + 2}.$$
 
 输出：