numpy 解一道简单数学题

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：

\[
\begin{bmatrix}
3 & 3.2 \\
3.5 & 3.6
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2 \\
\end{bmatrix}
=
\begin{bmatrix}
118.4 \\
135.2
\end{bmatrix}
\]

化为：

\[
\begin{bmatrix}
x_1 \\
x_2
\end{bmatrix}
=
{
\begin{bmatrix}
3 & 3.2 \\
3.5 & 3.6
\end{bmatrix}
}^{-1}
\begin{bmatrix}
118.4 \\
135.2
\end{bmatrix}
\]

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

\[
inverse\_a =
\begin{bmatrix}
-9 & 8 \\
8.75 & -7.5
\end{bmatrix}
\]

\[
result =
\begin{bmatrix}
16 \\
22
\end{bmatrix}
\]

也就是说是16个children，22个adults