python solve linear equation system code example

Example 1: solving linear equation using numpy

import numpy as np

a = np.array([[6,2,-5], [3,3,-2], [7,5,-3]])
b = np.array([13,13,26])
x = np.linalg.solve(a, b)

print(x)

Example 2: python system of equations

import numpy as np
A = np.array([[8, 3, -2], [-4, 7, 5], [3, 4, -12]])
b = np.array([9, 15, 35])
x = np.linalg.solve(A, b)
x

Example 3: solve linear system python

>>> a = np.array([[3,1], [1,2]])
>>> b = np.array([9,8])
>>> x = np.linalg.solve(a, b)
>>> x
array([2.,  3.])

Example 4: python linear equation components

def liner(x,y):
    """ 'y(x) = ax + b' --> get a & b by providing arrays x & y"""
    sum_xy = sum([i*j for i,j in zip(x,y)])
    sum_x2 = sum([pow(i,2)for i in x ])
    a = ( len(y)*sum_xy - sum(x)*sum(y) ) / ( len(y)*sum_x2 - pow(sum(x),2))  
    b = ( sum(y)*sum_x2 - sum(x)*sum_xy)  / ( len(y)*sum_x2 - pow(sum(x),2)) 
    return a,b
xx = [0,2,6,11,12,13,17,21,24,26,31,36,37]
yy = [0,4,7,11,16,26,27,31,39,47,49,57,58]
a,b = liner(xx,yy)
print("a:",a," b:",b)  # a: 1.631407787762088 b: -1.000941377834831

# Or use numpy
import numpy as np
np.polyfit(xx, yy, 1)   # [ 1.63140779 -1.00094138]