1 . 已知数表
,
,
,其中
,
,
分别表示
,
,
中第
行第
列的数.若
,则称
是
,
的生成数表.
(1)若数表
,
,且
是
,
的生成数表,求
;
(2)对
,
,
数表
,
,
与
满足第i行第j列的数对应相同(
).
是
,
的生成数表,且
.
(ⅰ)求
,
;
(ⅱ)若
恒成立,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9269360e275b7d80b6cdc272af8eedbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3703fa838be7c2c7ae3944fc24536cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5e30310b713914b2b021d9ffa89dee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223f93ed43c7772a367043ae224b75da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2cf56fabf5a66f4f99e499bf371846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b11e86b3abf5d95a36a9cc611534780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa4dbfb36335e29c3ebca8dca33d4e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03e28332446eea06a9bd61050d38373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67fcefc49af5da7ca9016c80e6a1ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03e28332446eea06a9bd61050d38373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b11e86b3abf5d95a36a9cc611534780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa4dbfb36335e29c3ebca8dca33d4e1.png)
(1)若数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7a413014cfac660883ba4bbb844b255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/025393abcedb4f6dd0b1be720a7b955f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647c97da671781944dcbac93af7cadcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/174541741f9d18ca1394943abd2ed0aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/403e9c8769f452f0c9e69a178b3c0cb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647c97da671781944dcbac93af7cadcb.png)
(2)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8365233f341451598eb50525a1557a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce60f9ae46219ff2567aa1470fd1a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd6a98dcb4b1455486e05a9141b8dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d946a5730d33d84577c7bc4a69b9e96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/160710545968157b392c210012e81ee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ffc1d9460ea481e699ed84da936250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f91d58007c604e83eb066e79e8cc88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b11e86b3abf5d95a36a9cc611534780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d946a5730d33d84577c7bc4a69b9e96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4e0386d1ce782d770ef7236edbea7c.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e542a1e1667a89ce2e20a2b52b42e359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7023dd3e3bac9a9b47e75d2976b0efab.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c96a64acdc0c29543dae62909b4e5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
解题方法
2 . 已知
是实常数,
.
(1)当
时,求函数
的单调增区间;
(2)是否存在
,使得
是与
有关的常数函数,求出所有满足条件的
,若不存在,说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc849f246ca0d82bac78beaf64b91c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9c5dcfff2f777dbac390c16d7cb4de4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354ac956269627cbd3c4088fe344014d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
3 . 已知矩阵
,且二阶矩阵M满足AMB,求M的特征值及属于各特征值的一个特征向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c08d989e2a396bffe179a0430e716d3.png)
您最近一年使用:0次
2020-04-09更新
|
110次组卷
|
2卷引用:北京市西城区第五十六中学2022届高三数学零模试题
名校
4 . 将所有平面向量组成的集合记作
,
是从
到
的对应关系,记作
或
,其中
、
、
、
都是实数,定义对应关系
的模为:在
的条件下
的最大值记作
,若存在非零向量
,及实数
使得
,则称
为
的一个特殊值;
(1)若
,求
;
(2)如果
,计算
的特征值,并求相应的
;
(3)若
,要使
有唯一的特征值,实数
、
、
、
应满足什么条件?试找出一个对应关系
,同时满足以下两个条件:①有唯一的特征值
,②
,并验证
满足这两个条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c85067c53e936ef32da818efe04bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5938410a3d39a1f3f4df67faf99ab5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39549972b3c02bd84637471fb171ae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6951a7aad8c0f5a06ad8bb6fb8f0f544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9c5e3816909bd49a229130af166698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e6644ad87b4054c76468bdf95baa8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/393f7419709b2c20d4234b63fc4c9fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6938ce64829c28318021579c6e45b4a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f17de8ca8bc0eeecd338e423f787e92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e6644ad87b4054c76468bdf95baa8f.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df049cbc7425555ea643fbb824a0df63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552355ddba8eef1ca3bf15eb53d79622.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2322e48ae3b2a166f061eb4aaf39f355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da66c64d70ef7d57d645e11f2a1b1e34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
您最近一年使用:0次
2020-02-13更新
|
635次组卷
|
3卷引用:2020届北京市第22中学高三第一学期第二次阶段性考试数学试题
名校
5 . 已知
、
是实常数,
.
(1)当
,
时,求函数
的最小正周期、单调增区间与最大值;
(2)是否存在
,使得
是与
有关的常数函数(即
的值与
的取值无关)?若存在,求出所有满足条件的
,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f5913e94cb3acf706be3a893abbbdb.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e2c8d466ab8eb5ecd38060b53bbe8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2019-11-11更新
|
186次组卷
|
3卷引用:北京市海淀区2022-2023学年高三下学期5月月考模拟数学试题
名校
6 . 已知二阶矩阵
,矩阵
属于特征值
的一个特征向量为
,属于特征值
的一个特征向量为
.求矩阵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed200695647fef921e0c4dcae71f938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4712ae924da953c4451dd78b8d6ac2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c240ca21dfe615b260aff275c63fd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278ddba8d8863b9cd1bb2d0ae292db78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48770a8b911fb7b155af453bf348e75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2019-07-16更新
|
347次组卷
|
6卷引用:北京市怀柔区2020届高三高考数学二模试题