print("Question 9")
import numpy as np
def FE(M):
    m,n=A.shape
    for i in range(n-1):
        for j in range(i+1,m):
            Ab[j,:]=Ab[j,:]-Ab[j,i]/Ab[i,i]*Ab[i,:]
    return Ab
def BS(Ab):
    m,n=Ab.shape
    n-=1
    x=np.empty(n)
    for i in range(n-1,-1,-1):
        sum=0
        for j in range (i+1,n):
            sum+=Ab[i,j]*x[j]
        x[i]=(Ab[i,n]-sum)/Ab[i,i]
    return x
def BE(M):
    m,n=A.shape
    for i in range (n-1,-1,-1):
        for j in range(0,i):
            Ab[j,:]=Ab[j,:]-Ab[j,i]/Ab[i,i]*Ab[i,:]
    return Ab
def gauss(Ab):
    Ab = FE(Ab)
    return BS(Ab)

def gaussjordan(Ab):
    Ab = FE(Ab)
    Ab=BE(Ab)
    return BS(Ab)
A = np.array([[4,-1,0,3],[-2,3,1,-5],[1,1,-1,2],[3,2,-4,0]],dtype=float)
b = np.array([[10,-3,2,4]],dtype=float).T
Ab = np.concatenate([A,b],1)
print(gauss(Ab))
print(gaussjordan(Ab))