#Gaussian Elimination 
# to solve Ax=b


import numpy as np

def gauss(a,b,x):
  N=len(a)
#reduce rows
  for i in range(N):
    for j in range(i+1,N):
      for k in range(i+1,N):
        a[j,k]-=a[j,i]*a[i,k]/a[i,i]
      b[j]-=b[i]*a[j,i]/a[i,i]
# back substitution
  temp=range(N)
  temp.reverse()
  for i in temp:
    for j in range(i+1,N): 
      b[i]-=a[i,j]*x[j]
    x[i]=b[i]/a[i,i]




a=np.loadtxt("matrix")
b=np.loadtxt("vector")
x=np.zeros(len(a))
gauss(a,b,x)
print x