#Gauss迭代法 輸入係數矩陣mx、值矩陣mr、迭代次數n(以list模擬矩陣 行優先)
def Gauss(mx,mr,n=100):
    if len(mx) == len(mr):  #若mx和mr長度相等則開始迭代 否則方程無解
        x = [] #迭代初值 初始化為單行全0矩陣
        for i in range(len(mr)):
            x.append([0])
        count = 0 #迭代次數計數
        while count < n:
            for i in range(len(x)):
                nxi = mr[i][0]
                for j in range(len(mx[i])):
                    if j!=i:
                        nxi = nxi+(-mx[i][j])*x[j][0]
                nxi = nxi/mx[i][i]
                x[i][0] = nxi
            count = count + 1
        return x 
    else:
        return False

#呼叫 Gauss(mx,mr,n=100) 示例
    

mx = [[8,-3,2],[4,11,-1],[6,3,12]]
mr = [[20],[33],[36]]
print(Gauss(mx,mr,20))