python svd法求解矩阵Ax=0最小二乘问题 拟合直线

为什么Ax=0的解是V的最后一列

import numpy as np
#随机矩阵 A
A=np.random.randint(1,25,[3,5])
u,sigma,vt = np.linalg.svd(A)
print(A@ vt[-1])

拟合直线：

def fitline(points):
	#ax+by+c=0
	#solve Ax =0:
	#ax0+by0+c=0
	#ax1+by1+c=0
	#ax2+by2+c=0
	#...
	points = np.concatenate((points, np.ones(len(points)).reshape(-1, 1)),axis=1)
	u,sigma,vt = np.linalg.svd(points)
	v= np.transpose(vt)
	return vt[-1]

计算：

x= np.arange(0,100)
x = x.reshape(-1,1)
y =2*x +1
points=np.column_stack((x,y))
print(fitline(points))

结果：

[ 0.81649658 -0.40824829  0.40824829]