1 . 将所有平面向量组成的集合记作
,
是从
到
的映射,记作
或
,其中
,
,
,
,
,
,都是实数.定义映射
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
的一个特征值.
(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?试找出一个映射
,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/02de2ea205a54acd8cd7e279b96d1c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39549972b3c02bd84637471fb171ae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0b2929e18e7737669e001ec83b4543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f921a664a3f2a8696f7702bb38ad61f.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/da1a9fb3904514272b50fa3339ee2b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9c5e3816909bd49a229130af166698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edbc4c88fe1a586aef39e92e925f0337.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ad9a98e9aae2623ea32b1b05960470.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/a072f92e9330b67545633ef422c3ee2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edbc4c88fe1a586aef39e92e925f0337.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72819d3bcd97399a6ed89f87efaa92b0.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/a668834bb908d31cb0fac925c1c9dd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
您最近一年使用:0次
2022-03-04更新
|
779次组卷
|
4卷引用:安徽省芜湖市安徽师范大学附属中学2023-2024学年高一下学期3月阶段性教学质量监测数学试题
名校
解题方法
2 . 设奇函数
的定义域为
,且
的图象是连续不间断,
,有
,若
,则
的取值范围是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a80708bb56041678e6256ca37ec2355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd6e432d312946ca4807166e1c09799a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/101b2d8ee03f0af91f1ce3f0cc1bd8dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092ef9bde62fef299e7e74f6e4be4941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-08-06更新
|
1134次组卷
|
6卷引用:安徽省六安市第一中学2019-2020学年高二下学期期中数学(理)试题
安徽省六安市第一中学2019-2020学年高二下学期期中数学(理)试题安徽省六安市城南中学2020-2021学年高三上学期第三次月考数学(理)试题(已下线)专题2-3 导数压轴小题归类(讲+练)-3江西省湖口中学2022-2023学年高二下学期5月期中考试数学试题(已下线)专题2-4 构造函数以及切线-2(已下线)专题2-4 构造函数以及切线-2
2013高三·安徽·竞赛
3 . 设a、b、c是不全为0的实数.求
的取值范围a、b、c分别满足什么条件时,F取最大值与最小值?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503138cbbc6aca6e66fc65b134ec2c2d.png)
您最近一年使用:0次
2006高三·安徽·竞赛
4 . 若关于 x 的方程
恰有一个实根,则 k 的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21510696899130715a6236c666cef548.png)
您最近一年使用:0次
5 . 设集合
,
,映射
使对任意
都有
是奇数.则这样的映射
的个数是.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d8472ddb9227af5195aac27bd3f6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e49522e18ab967bb09c6790c314bdfa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a662f934b3bf3ad6f1f1414fedb381d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2fa6dee4e0287c40e5c3e7e000f01c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
A.45 | B.27 | C.15 | D.11 |
您最近一年使用:0次
2018-12-16更新
|
255次组卷
|
3卷引用:2005年安徽省高中数学竞赛初赛试题