下载两个安装包并解压:

配置jdk环境变量:

[root@VM-0-10-centos zookeeper]# cat /root/.bash_profile
# .bash_profile # Get the aliases and functions
if [ -f ~/.bashrc ]; then
. ~/.bashrc
fi # User specific environment and startup programs #PATH=$PATH:$HOME/bin:$JAVA_HOME JAVA_HOME=/home/zookeeper/jdk1.8.0_131/ export JAVA_HOME
PATH=$PATH:$HOME/bin:$JAVA_HOME
export PATH

测试jkd是否生效:

[root@VM-0-10-centos zookeeper]# java -version
java version "1.8.0_131"
Java(TM) SE Runtime Environment (build 1.8.0_131-b11)
Java HotSpot(TM) 64-Bit Server VM (build 25.131-b11, mixed mode)

进如zookeeper配置目录,编写配置文件:

[root@VM-0-10-centos conf]# cp zoo_sample.cfg zoo.cfg

建立zookeepr数据目录
[root@VM-0-10-centos data]# pwd
/home/zookeeper/zookeeper-3.4.10/data

配置文件:

启动查看状态:

[root@VM-0-10-centos bin]# pwd
/home/zookeeper/zookeeper-3.4.10/bin
[root@VM-0-10-centos bin]# sh zkServer.sh start
ZooKeeper JMX enabled by default
Using config: /home/zookeeper/zookeeper-3.4.10/bin/../conf/zoo.cfg
Starting zookeeper ... STARTED
[root@VM-0-10-centos bin]# sh zkServer.sh status
ZooKeeper JMX enabled by default
Using config: /home/zookeeper/zookeeper-3.4.10/bin/../conf/zoo.cfg
Mode: standalone
[root@VM-0-10-cent

登陆:

[root@VM-0-10-centos bin]# pwd
/home/zookeeper/zookeeper-3.4.10/bin
[root@VM-0-10-centos bin]# sh zkCli.sh
Connecting to localhost:2181

zookeeper常用的Shell命令:

新增节点

格式:节点的路径  节点的数据

create [-s] [-e] path data #其中-s 为有序节点,-e 临时节点

注意:默认什么都不加的是无序持久节点

登陆服务器:

新增一个持久化节点,默认就是持久化节点
[zk: localhost:2181(CONNECTED) 0] create /hadoop "1234"
Created /hadoop
查看节点的数据
[zk: localhost:2181(CONNECTED) 1] get /hadoop
1234
cZxid = 0x6
ctime = Sat Sep 05 15:05:31 CST 2020
mZxid = 0x6
mtime = Sat Sep 05 15:05:31 CST 2020
pZxid = 0x6
cversion = 0
dataVersion = 0
aclVersion = 0
ephemeralOwner = 0x0
dataLength = 4
numChildren = 0

创建持久化有序节点:

应用场景:为分布式环境创建一个唯一id

[zk: localhost:2181(CONNECTED) 1] create  -s /a  "aaaa"
Created /a0000000001
[zk: localhost:2181(CONNECTED) 2] get /a0000000001
aaaa
cZxid = 0x9
ctime = Sat Sep 05 15:09:10 CST 2020
mZxid = 0x9
mtime = Sat Sep 05 15:09:10 CST 2020
pZxid = 0x9
cversion = 0
dataVersion = 0
aclVersion = 0
ephemeralOwner = 0x0
dataLength = 4
numChildren = 0
[zk: localhost:2181(CONNECTED) 3] get /a
Node does not exist: /a

注意:创建时候的路径名字不再是获取数据的哪个名字,a---->a00000001

创建临时节点:

与会话共存亡

[zk: localhost:2181(CONNECTED) 4] create -e /tmp  "tmp"
Created /tmp
[zk: localhost:2181(CONNECTED) 5] get /tmp
tmp
cZxid = 0xa
ctime = Sat Sep 05 15:13:15 CST 2020
mZxid = 0xa
mtime = Sat Sep 05 15:13:15 CST 2020
pZxid = 0xa
cversion = 0
dataVersion = 0
aclVersion = 0
ephemeralOwner = 0x1745d11ec160002
dataLength = 3
numChildren = 0

注意:登陆后不存在

临时有序节点

临时节点会在会话过期后被删除,建立分布式锁

[zk: localhost:2181(CONNECTED) 6] create -s -e /quan "quan"
Created /quan0000000003
[zk: localhost:2181(CONNECTED) 7] get /quan0000000003
quan
cZxid = 0xb
ctime = Sat Sep 05 15:15:11 CST 2020
mZxid = 0xb
mtime = Sat Sep 05 15:15:11 CST 2020
pZxid = 0xb
cversion = 0
dataVersion = 0
aclVersion = 0
ephemeralOwner = 0x1745d11ec160002
dataLength = 4
numChildren = 0

修改节点

格式1

set  节点路径  新的节点的值
[zk: localhost:2181(CONNECTED) 8] get /hadoop
1234
cZxid = 0x6
ctime = Sat Sep 05 15:05:31 CST 2020
mZxid = 0x6
mtime = Sat Sep 05 15:05:31 CST 2020
pZxid = 0x6
cversion = 0
dataVersion = 0
aclVersion = 0
ephemeralOwner = 0x0
dataLength = 4
numChildren = 0
[zk: localhost:2181(CONNECTED) 9] set /hadoop "879"
cZxid = 0x6
ctime = Sat Sep 05 15:05:31 CST 2020
mZxid = 0xc
mtime = Sat Sep 05 15:17:35 CST 2020
pZxid = 0x6
cversion = 0
dataVersion = 1
aclVersion = 0
ephemeralOwner = 0x0
dataLength = 3
numChildren = 0
[zk: localhost:2181(CONNECTED) 10] get /hadoop
879
cZxid = 0x6
ctime = Sat Sep 05 15:05:31 CST 2020
mZxid = 0xc
mtime = Sat Sep 05 15:17:35 CST 2020
pZxid = 0x6
cversion = 0
dataVersion = 1

格式2

基于版本号进行更改,此时类似于乐观锁机制,当你传入的数据版本号
(dataVersion) 和当前节点的数据版本号不符合时,zookeeper 会拒绝本次修改:
可以联想一些关系型数据库来理解

注意:第一次创建的节点,节点信息会附带一个信息,就是dataversion,从0开始

每一次修改都会+1

[zk: localhost:2181(CONNECTED) 11] set /hadoop "2222" 0
version No is not valid : /hadoop
[zk: localhost:2181(CONNECTED) 12] set /hadoop "2222" 1
cZxid = 0x6
ctime = Sat Sep 05 15:05:31 CST 2020
mZxid = 0xe
mtime = Sat Sep 05 15:23:13 CST 2020
pZxid = 0x6
cversion = 0
dataVersion = 2
aclVersion = 0
ephemeralOwner = 0x0
dataLength = 4
numChildren = 0

删除节点:

格式:

delete path [version]
和更新节点数据一样,也可以传入版本号,当你传入的数据版本号 (dataVersion)
和当前节点的数据版本号不符合时,zookeeper 不会执行删除操作。
[zk: localhost:2181(CONNECTED) 13] delete  /hadoop
[zk: localhost:2181(CONNECTED) 16] get /hadoop
Node does not exist: /hadoop
[zk: localhost:2181(CONNECTED) 17] create /hadoop "99"
Created /hadoop
[zk: localhost:2181(CONNECTED) 18] get /hadoop
99
cZxid = 0x10
ctime = Sat Sep 05 15:25:31 CST 2020
mZxid = 0x10
mtime = Sat Sep 05 15:25:31 CST 2020
pZxid = 0x10
cversion = 0
dataVersion = 0
aclVersion = 0
ephemeralOwner = 0x0
dataLength = 2
numChildren = 0
[zk: localhost:2181(CONNECTED) 19] delete /hadoop 1
version No is not valid : /hadoop
[zk: localhost:2181(CONNECTED) 20] delete /hadoop 0
[zk: localhost:2181(CONNECTED) 21] get /hadoop
Node does not exist: /hadoop

注意:要想删除某个节点及其所有后代节点,可以使用递归删除,命令为 rmr

[zk: localhost:2181(CONNECTED) 22] create /hadoop "99"
Created /hadoop
[zk: localhost:2181(CONNECTED) 23] create /hadoop/son "998"
Created /hadoop/son
[zk: localhost:2181(CONNECTED) 24] get /hadoop
99
cZxid = 0x13
ctime = Sat Sep 05 15:27:07 CST 2020
mZxid = 0x13
mtime = Sat Sep 05 15:27:07 CST 2020
pZxid = 0x14
cversion = 1
dataVersion = 0
aclVersion = 0
ephemeralOwner = 0x0
dataLength = 2
numChildren = 1
[zk: localhost:2181(CONNECTED) 25] get /hadoop/son
998
cZxid = 0x14
ctime = Sat Sep 05 15:27:16 CST 2020
mZxid = 0x14
mtime = Sat Sep 05 15:27:16 CST 2020
pZxid = 0x14
cversion = 0
dataVersion = 0
aclVersion = 0
ephemeralOwner = 0x0
dataLength = 3
numChildren = 0
[zk: localhost:2181(CONNECTED) 26] del delquota delete
[zk: localhost:2181(CONNECTED) 26] del delquota delete
[zk: localhost:2181(CONNECTED) 26] delete /hadoop
Node not empty: /hadoop
[zk: localhost:2181(CONNECTED) 27] rmr /hadoop

查看节点:

格式:

get path
[zk: localhost:2181(CONNECTED) 29] get /hadoop
99
cZxid = 0x18 数据节点创建时的事务ID
ctime = Sat Sep 05 15:29:57 CST 2020 创建时的时间
mZxid = 0x18 最后一次更新时的事务ID
mtime = Sat Sep 05 15:29:57 CST 2020 最后一次更新时的时间
pZxid = 0x18 数据节点的子节点最后一次被修改时的事务ID
cversion = 0 子节点的更改次数
dataVersion = 0 节点数据的更改次数即版本数
aclVersion = 0 节点的ACL的更改次数
ephemeralOwner = 0x0 临时节点,表示创建该节点的会话SessionID,持久节点,改属性为0
dataLength = 2 数据内容长度
numChildren = 0 数据节点当前的子节点个数

注意:Zxid(ZooKeeper TransactionId),ZooKeeper 节点的每一次更改都具有唯一的 Zxid

如果 Zxid1 小于 Zxid2,则Zxid1 的更改发生在 Zxid2 更改之前

查看节点状态

可以使用 stat 命令查看节点状态,它的返回值和 get 命令类似,但不会返回
节点数据

[zk: localhost:2181(CONNECTED) 30] stat /hadoop
cZxid = 0x18
ctime = Sat Sep 05 15:29:57 CST 2020
mZxid = 0x18
mtime = Sat Sep 05 15:29:57 CST 2020
pZxid = 0x18
cversion = 0
dataVersion = 0
aclVersion = 0
ephemeralOwner = 0x0
dataLength = 2
numChildren = 0

查看节点列表

ls  path   返回当前节点的子节点列表
ls2 path 放回当前节点的子节点列表和当前节点的状态信息
[zk: localhost:2181(CONNECTED) 33] ls /hadoop
[qq1, qq2]
[zk: localhost:2181(CONNECTED) 34] ls2 /hadoop
[qq1, qq2]
cZxid = 0x18
ctime = Sat Sep 05 15:29:57 CST 2020
mZxid = 0x18
mtime = Sat Sep 05 15:29:57 CST 2020
pZxid = 0x1a
cversion = 2
dataVersion = 0
aclVersion = 0
ephemeralOwner = 0x0
dataLength = 2
numChildren = 2

监听器:一次性用品,用完就没有了,要重新买

get path [watch]

注册的监听器能够在节点内容发生改变的时候,向客
户端发出通知。需要注意的是 zookeeper 的触发器是一次性的 (One-time trigger),即
触发一次后就会立即失效。

stat path [watch]

注册的监听器能够在节点状态发生改变的时候,向客户端发出通知

ls/ls2 path [watch]

使用 ls path [watch] 或 ls2 path [watch] 注册的监听器能够监听该节点下所有子节点的增加和删除操作。

Zookeeper的ACL权限控制

zookeeper的access control list 访问控制列表

acl 权限控制,使用scheme:id:permission 来标识

权限模式(scheme):授权的策略
授权对象(id):授权的对象
权限(permission):授予的权限 规则
1zooKeeper的权限控制是基于每个znode节点的,需要对每个节点设置权限
2每个znode支持设置多种权限控制方案和多个权限
3子节点不会继承父节点的权限,客户端无权访问某节点,可能可以访问它的子节点

权限模式scheme

方案                 描述
world 只有一个用户:anyone,代表登录zokeeper所有人(默认)
ip 对客户端使用IP地址认证
auth 使用已添加认证的用户认证---可以是明文密码
digest 使用“用户名:密码”方式认证--密文密码

授权对象:

授权对象ID是指,权限赋予的实体,

例如:IP 地址或用户或者anyone

授予的权限

create

delete

read

writer

admin

也就是 增、删、改、查、管理权限,这5种权限简写为cdrwa,

注意:这5种权限中,delete是指对子节点的删除权限,其它4种权限指对自身节点的操作权限

授权相关命令:

命令格式:

setAcl  节点  授权模式:授权对象:授权权限

练习:

word模式

新建节点
[zk: localhost:2181(CONNECTED) 5] create /node1 "node1"
Created /node1
查看默认的权限
[zk: localhost:2181(CONNECTED) 6] getAcl /node1
'world,'anyone
: cdrwa
新创建的节点的子节点
[zk: localhost:2181(CONNECTED) 7] create /node1/node11 "node11"
Created /node1/node11
[zk: localhost:2181(CONNECTED) 8] create /node1/node22 "node22"
Created /node1/node22
[zk: localhost:2181(CONNECTED) 9] ls /node1
[node11, node22]
修改节点权限为不能添加子节点
[zk: localhost:2181(CONNECTED) 10] setAcl /node1 world:anyone:drwa
cZxid = 0x20
ctime = Sat Sep 05 16:11:38 CST 2020
mZxid = 0x20
mtime = Sat Sep 05 16:11:38 CST 2020
pZxid = 0x22
cversion = 2
dataVersion = 0
aclVersion = 1
ephemeralOwner = 0x0
dataLength = 5
numChildren = 2
[zk: localhost:2181(CONNECTED) 11] getAcl /node1
'world,'anyone
: drwa
添加子节点失败
[zk: localhost:2181(CONNECTED) 12] create /node1/node33 "node33"
Authentication is not valid : /node1/node33
[zk: localhost:2181(CONNECTED) 13]

IP授权模式

格式:

setAcl <path> ip:<ip>:<acl>

注意:zkCli.sh -server ip

Auth授权模式

addauth digest <user>:<password> #添加认证用户
setAcl <path> auth:<user>:<acl>

注意:必须先进行授权认证用户的添加

[zk: localhost:2181(CONNECTED) 13] create /node3  "node3"
Created /node3
[zk: localhost:2181(CONNECTED) 14] getAcl /node3
'world,'anyone
: cdrwa 添加认证用户密码
[zk: localhost:2181(CONNECTED) 15] addauth digest quan:1234
设置acl auth模式的权限
[zk: localhost:2181(CONNECTED) 16] setAcl /node3 auth:quan:cdrwa
cZxid = 0x26
ctime = Sat Sep 05 16:27:56 CST 2020
mZxid = 0x26
mtime = Sat Sep 05 16:27:56 CST 2020
pZxid = 0x26
cversion = 0
dataVersion = 0
aclVersion = 1
ephemeralOwner = 0x0
dataLength = 5
numChildren = 0
查看权限
[zk: localhost:2181(CONNECTED) 17] getAcl /node3
'digest,'quan:oEBCQutcK+DX5snUyMCk9GdEdbY=
: cdrwa
[zk: localhost:2181(CONNECTED) 0] get /node3
Authentication is not valid : /node3
[zk: localhost:2181(CONNECTED) 1] addauth digest quan:12345
[zk: localhost:2181(CONNECTED) 2] get /node3
Authentication is not valid : /node3
[zk: localhost:2181(CONNECTED) 3] addauth digest quan:123
[zk: localhost:2181(CONNECTED) 4] get /node3
Authentication is not valid : /node3
需要添加正确的账号密码才能查看
[zk: localhost:2181(CONNECTED) 5] addauth digest quan:1234
[zk: localhost:2181(CONNECTED) 6] get /node3
node3
cZxid = 0x26
ctime = Sat Sep 05 16:27:56 CST 2020
mZxid = 0x26
mtime = Sat Sep 05 16:27:56 CST 2020
pZxid = 0x26
cversion = 0
dataVersion = 0
aclVersion = 1
ephemeralOwner = 0x0
dataLength = 5
numChildren = 0

Digest授权模式

格式:

setAcl <path> digest:<user>:<password>:<acl>

注意:密码是经过SHA1及BASE64处理的密文,在SHELL中可以通过以下命令计算

echo -n <user>:<password> | openssl dgst -binary -sha1 | openssl base64
[root@VM-0-10-centos data]# echo -n quan:1234 |openssl dgst -binary -sha1 |openssl base64
oEBCQutcK+DX5snUyMCk9GdEdbY=

授权

[zk: localhost:2181(CONNECTED) 7] create /node4 "node4"
Created /node4
[zk: localhost:2181(CONNECTED) 8] getAcl /node4
'world,'anyone
: cdrwa
[zk: localhost:2181(CONNECTED) 9] setAcl /node4 digest:quan:oEBCQutcK+DX5snUyMCk9GdEdbY=:cdrwa
cZxid = 0x2a
ctime = Sat Sep 05 16:38:27 CST 2020
mZxid = 0x2a
mtime = Sat Sep 05 16:38:27 CST 2020
pZxid = 0x2a
cversion = 0
dataVersion = 0
aclVersion = 1
ephemeralOwner = 0x0
dataLength = 5
numChildren = 0
[zk: localhost:2181(CONNECTED) 10] getAcl /node4
'digest,'quan:oEBCQutcK+DX5snUyMCk9GdEdbY=
: cdrwa

多种模式授权

[zk: localhost:2181(CONNECTED) 25] getAcl /node555
Node does not exist: /node555
[zk: localhost:2181(CONNECTED) 26] create /node555 "node555"
Created /node555
[zk: localhost:2181(CONNECTED) 27] getAcl /node555
'world,'anyone
: cdrwa
[zk: localhost:2181(CONNECTED) 28] setAcl /node555 ip:192.168.1.120:cdre,auth:qq:cdrwa,digest:qq:oEBCQu
Unknown perm type: e
cZxid = 0x32
ctime = Sat Sep 05 16:45:23 CST 2020
mZxid = 0x32
mtime = Sat Sep 05 16:45:23 CST 2020
pZxid = 0x32
cversion = 0
dataVersion = 0
aclVersion = 1
ephemeralOwner = 0x0
dataLength = 7
numChildren = 0
[zk: localhost:2181(CONNECTED) 29] getAcl /node555
'ip,'192.168.1.120
: cdr
'digest,'qq:oEBCQutcK+DX5snUyMCk9GdEdbY=
: cdrwa
'digest,'quan:M593vXym1b1qBYmZzb9KjzJUYPY=
: cdrwa
'digest,'quan:99P5xbaTA/8xWBtZZ6O50EznJ2g=
: cdrwa
'digest,'quan:oEBCQutcK+DX5snUyMCk9GdEdbY=
: cdrwa
'digest,'quan:Ux4TTJ10q7ejbdzki3X+T/mIkBY=
: cdrwa
'digest,'qq:3CK5BvP+nSNTC8vS4NgrdptCQdk=
: cdrwa
[zk: localhost:2181(CONNECTED) 30]

ACL超级管理园:

在zkServer.sh文件的nohup哪一行的\号之前加入

"-
Dzookeeper.DigestAuthenticationProvider.superDigest=super:xQJmxLMiHGwaqBv
st5y6rkB6HQs="

行号的密码自己用上面的生成

addauth digest super:admin #添加认证用户

linux-安装zookeeper及相关操作的更多相关文章

  1. Linux 安装Zookeeper<准备>(使用Mac远程访问)

    阅读本文需要安装JDK 一 Zookeeper简介 zookeeper是用java语言编写的一款为分布式应用所设计的协调服务 zookeeper是apacahe hadoop的子项目 使用zookee ...

  2. linux安装zookeeper及使用

    一.安装条件 想要安装zookeeper,必须先在linux中安装好jdk.安装步骤见: https://www.cnblogs.com/expiator/p/9987351.html 二.下载并解压 ...

  3. Docker安装Zookeeper并进行操作

    Docker安装Zookeeper 下载Zookeeper镜像docker pull zookeeper1启动容器并添加映射docker run --privileged=true -d --name ...

  4. Mysql安装和登录相关操作

    一.mysql的下载和安装 1.下载链接地址 http://dev.mysql.com/downloads/mysql/ 安装如下操作进行下载. 2.mysql数据库安装(Windows环境) 1.解 ...

  5. linux安装Zookeeper及redis集群

    亲测有效: 1.linux下安装zookeeper:https://www.cnblogs.com/zuolun2017/p/8186254.html 2.linux下安装redis集群:https: ...

  6. Linux 安装Zookeeper<集群版>(使用Mac远程访问)

    阅读本文需要先阅读安装Zookeeper<准备> 一 架构细节 zookeeper集群根据投票选举的机制 选出leader和follower zookeeper集群节点建议是奇数 这里我准 ...

  7. Linux 安装Zookeeper<单机版>(使用Mac远程访问)

    阅读本文需要先阅读安装Zookeeper<准备> 新建目录 mkdir /usr/local/zookeeper 解压 cd zookeeper压缩包所在目录 tar -xvf zooke ...

  8. linux常用命令---用户相关操作

    用户相关操作

  9. Linux之CentOS下vsftp安装及配置相关操作

    1.安装ftps——vsftpd: #yum install vsftpd 2.指定上传下载目录配置: 如:用户名:xxx,需指定目录:/xxx/xxx #useradd -d /xxx/xxx -s ...

  10. 【转】SVN linux命令及 windows相关操作(一)

    从以下博客转载和整理: http://www.cnblogs.com/richcem/archive/2011/01/08/1930823.html http://blog.wpjam.com/m/t ...

随机推荐

  1. RFC2899广播吞吐量测试——网络测试仪实操

    一.简介 RFC 2889为LAN交换设备的基准测试提供了方法学,它将RFC 2544中为网络互联设备基准测试所定义的方法学扩展到了交换设备,提供了交换机转发性能(Forwarding Perform ...

  2. 在windev中实现BS架构级的灵活排版

    windev是CS架构,但却能够实现BS架构级的灵活排版.玩过CS架构的老铁们,感受应会都如我,如获新生!因为苦于没有一张好画皮久矣!在windev中,要实现灵活,专业,自适应和非常丰富的排版,可以关 ...

  3. 【Java分享客栈】我有一个朋友,和前端工程师联调接口被狠狠鄙视了一番。

    前言 我有一个朋友,昨天和前端工程师联调一个接口,然后被狠狠鄙视了一番. 大家知道,自从前后端分离以后,像我一样一直以Java工程师为傲而自居的码圣们就砍掉了一半脊梁,从此被贴上了"Java ...

  4. 【C# .Net GC】自动内存管理

    原文:https://docs.microsoft.com/zh-cn/dotnet/standard/automatic-memory-management 自动内存管理是公共语言运行时在托管执行过 ...

  5. 45个 GIT 经典操作场景,专治不会合代码

    大家好,我是小富~ 技术交流关注公众号:程序员内点事 传送门:原文地址 git对于大家应该都不太陌生,熟练使用git已经成为程序员的一项基本技能,尽管在工作中有诸如 Sourcetree这样牛X的客户 ...

  6. MyBatis核心对象

    MyBatis 有三个基本要素: 核心接口和类 MyBatis核心配置文件(mybatis-config.xml) SQL映射文件(mapper.xml) 下面首先介绍 MyBatis 的核心接口和类 ...

  7. 自己写了个Java RMI(远程方法调用)的实现案例

    自己简单写了个Java RMI(远程方法调用)的实现案例. 为了更好理解RMI(远程方法调用).序列化的意义等等,花费三天多的时间肝了一个Java RMI的实现案例. !!!高能预警!!! 代码量有点 ...

  8. Python的介绍与主要方向

    1.1 编程与编程语言 python是一门编程语言,作为学习python的开始,需要事先搞明白:编程的目的是什么?什么是编程语言?什么是编程? 编程的目的: 计算机的发明,是为了用机器取代/解放人力, ...

  9. WPF优秀组件推荐之LiveCharts

    概述 LiveCharts是一个比较漂亮的WPF图表控件,在数据变化时还会有动画切换的效果,并且样式也可以控制. 官方网站:Live Charts (lvcharts.net) 开源代码:GitHub ...

  10. [USACO20FEB]Equilateral Triangles P 题解

    优雅的暴力. 设三个点为 \((i,j,k)\),则有 \(6\) 个未知数即 \(x_i,x_j,x_k,y_i,y_j,y_k\).又因为有 \(2\) 条关于这 \(6\) 个未知数的方程 \( ...