题目
A group took a trip on a bus, at 3 per child and 3.20 per adult for a total of 118.40.
They took the train back at 3.50 per child and 3.60 per adult for a total of 135.20.
How many children, and how many adults?
求解过程
设有x1个children,x2个adults，线性方程组为：
\[3x_1+3.2x_2 = 118.4
\]
\]
\[3.5x_1+3.6x_2 = 135.2
\]
\]
矩阵形式表示为：
\[\begin{bmatrix}
3 & 3.2 \\
3.5 & 3.6
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2 \\
\end{bmatrix}
=
\begin{bmatrix}
118.4 \\
135.2
\end{bmatrix}
\]
3 & 3.2 \\
3.5 & 3.6
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2 \\
\end{bmatrix}
=
\begin{bmatrix}
118.4 \\
135.2
\end{bmatrix}
\]
化为：
\[\begin{bmatrix}
x_1 \\
x_2
\end{bmatrix}
=
{
\begin{bmatrix}
3 & 3.2 \\
3.5 & 3.6
\end{bmatrix}
}^{-1}
\begin{bmatrix}
118.4 \\
135.2
\end{bmatrix}
\]
x_1 \\
x_2
\end{bmatrix}
=
{
\begin{bmatrix}
3 & 3.2 \\
3.5 & 3.6
\end{bmatrix}
}^{-1}
\begin{bmatrix}
118.4 \\
135.2
\end{bmatrix}
\]
接下来就是使用numpy求解了
代码
import numpy as np
a = np.matrix('3. 3.2;3.5,3.6')
b = np.matrix('118.4;135.2')
inverse_a = np.linalg.inv(a)
print(inverse_a)
result = inverse_a * b
print(result)
结果
\[inverse\_a =
\begin{bmatrix}
-9 & 8 \\
8.75 & -7.5
\end{bmatrix}
\]
\begin{bmatrix}
-9 & 8 \\
8.75 & -7.5
\end{bmatrix}
\]
\[result =
\begin{bmatrix}
16 \\
22
\end{bmatrix}
\]
\begin{bmatrix}
16 \\
22
\end{bmatrix}
\]
也就是说是16个children，22个adults