题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063913-22323.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063913-81943.gif)
中每行的数互不相同,前6列中每列的三数之和为1,
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063914-61105.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063914-58363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063914-86725.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063914-79009.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063915-56970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063915-42438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063915-86797.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063915-29314.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063916-80526.gif)
满足下面的性质
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063916-45363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063915-29314.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063916-56404.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063917-67394.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063917-32761.gif)
使得
⑶
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063917-53595.gif)
求证:
(ⅰ)最小值
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063917-56992.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-53607.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-70512.gif)
(ⅱ)存在数表
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063915-29314.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-70972.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-50532.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063919-20988.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063919-42237.gif)
仍然具有性质
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063916-45363.gif)
答案
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063919-39773.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-53607.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-70512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063919-26907.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063919-91678.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-53607.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063915-29314.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063920-67889.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-53607.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-70512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063916-45363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063920-73333.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063920-93838.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063921-43065.gif)
(ⅱ)由抽届原理知
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063921-54078.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063921-16162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063921-25009.gif)
中至少有两个值取在同一列.不妨设
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063921-15183.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063922-64525.gif)
由前面的结论知数表
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-70512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063919-26907.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063922-11735.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063919-26907.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-53607.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063922-84193.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063922-21496.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063919-26907.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-70512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063916-80526.gif)
记
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063923-44173.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063923-70990.gif)
显然
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063923-40811.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063923-24700.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063914-79009.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063924-16353.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063924-87215.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063924-82094.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063924-39115.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063925-40811.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063925-39087.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-50532.gif)
下面证明
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063919-20988.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063919-42237.gif)
具有性质
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063916-45363.gif)
从上面的选法可知
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063925-82723.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063925-11323.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063925-10059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063926-33255.gif)
又由
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-70512.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063916-45363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063926-22312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063926-42296.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063927-63028.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063927-39219.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-53607.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063927-33975.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063927-30917.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063918-53607.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063928-12553.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063928-27813.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063928-63983.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063916-45363.gif)
下证唯一性.设有
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063927-39219.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063928-56632.gif)
具有性质
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063916-45363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063928-33976.gif)
⑷
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063929-78992.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063929-61816.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063929-88501.gif)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063929-88501.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063929-80727.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063930-46009.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063930-99998.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063930-24901.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063930-17000.gif)
如果
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063930-99998.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063931-40809.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063916-45363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063930-46009.gif)
⑸
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063931-39601.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063930-24901.gif)
由数表
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063931-40809.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063916-45363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063931-23354.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063917-32761.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063931-28024.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063925-40811.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063932-21695.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063932-52469.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063932-58835.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063928-63983.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063916-45363.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063927-39219.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063932-50782.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063933-35192.gif)
核心考点
试题【在非负数构成的数表中每行的数互不相同,前6列中每列的三数之和为1,,,,,,,均大于.如果的前三列构成的数表满足下面的性质:对于数表中的任意一列(,2,…,9)】;主要考察你对常见矩阵变换等知识点的理解。[详细]
举一反三
(1)(本小题满分7分)选修4-2:矩阵与变换
已知向量
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063852-68882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063852-99900.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063853-82759.gif)
作用下得到点P′(3,3),求A4
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063852-68882.gif)
(2)(本小题满分7分)选修4-4:坐标系与参数方程
直线
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063853-84158.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063853-76875.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063853-82427.gif)
P(-1,0),且|PA|:|PB|=1:2,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063853-82427.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063854-34734.jpg)
(3)(本小题满分7分)选修4-5:不等式选讲
对于x∈R,不等式|x-1|+|x-2|≥
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063854-99353.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063854-61390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063854-99353.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063854-61390.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108063847-27810.jpg)