1 . 【选做题】
A.[选修4-2:矩阵与变换]
已知m,n∈R,向量
是矩阵
的属于特征值3的一个特征向量,求矩阵M及另一个特征值.
B.[选修4-4:坐标系与参数方程]
在平面直角坐标系xOy中,已知直线
的参数方程为
( t为参数),椭圆C的参数方程为
.设直线
与椭圆C交于A,B两点,求线段AB的长.
C.[选修4-5:不等式选讲]
已知x,y,z均是正实数,且
求证:
.
A.[选修4-2:矩阵与变换]
已知m,n∈R,向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e2afd5c369e410b7cf77cf4356d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685b3f58afdaea4a4d1df20cf6105fb0.png)
B.[选修4-4:坐标系与参数方程]
在平面直角坐标系xOy中,已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3f5611a1696924cfa2b8e4b8f693ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e962a73039db4ade7ed77bdd661719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
C.[选修4-5:不等式选讲]
已知x,y,z均是正实数,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ccf64ca4c82b41f0929a958a85d4f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f362d9633c6a8637a6b859c235efdf0f.png)
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真题
2 . 已知矩阵A的逆矩阵
,求矩阵A的特征值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7da97b363bfda2e80c1b987cab2349.png)
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名校
3 . 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)
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2019-07-16更新
|
347次组卷
|
6卷引用:2020届江苏省镇江市九校高三下学期3月模拟考试数学试题
4 . 已知矩阵A=
,满足A
=
,求矩阵A的特征值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce108a2e47d3bfdab27fa456dedc093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c79c23bb0fbba11cc94b17eccb2335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fef8aaa9bb5fb8a7de45a844d3e6602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f67a94047d640cfc40a9e9b23eded92.png)
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2019-01-29更新
|
334次组卷
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3卷引用:【市级联考】江苏省扬州市2019届高三第一次模拟考试 数学试题
5 . 已知矩阵
的一个特征值为4,求矩阵A的逆矩阵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8f53d0909c9e76968f7322c6be1dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a84646168f0afc4380043a52b818c35.png)
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2020-02-28更新
|
222次组卷
|
7卷引用:2020届江苏省无锡市天一中学高三第一次模拟考试数学试题
6 . 选修4—2 矩阵与变换
已知
,矩阵
有一个属于特征值
的特征向量
,
(1)求矩阵
;
(2)若矩阵
,求
.
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4abe69124805bf9da434f9a9488858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c2ece46e612f9042eafb3dd42a72e3.png)
(1)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a6cfd59046039eaae3a49616fb06b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6994cca5b8df73b467ce079d3bc68dd5.png)
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7 . 已知矩阵
,对应的变换把点
变成点
.
(1)求a,b的特征值;
(2)求矩阵M的特征值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c256127e5b93a9716e9a6ba36602372e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de468be0b50fe534b05e88db0d4fb88.png)
(1)求a,b的特征值;
(2)求矩阵M的特征值.
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2020-05-15更新
|
176次组卷
|
3卷引用:2020届江苏省南通市高三下学期5月模拟考试数学试题
8 . 已知矩阵
,
.
的逆矩阵
满足
.
(1)求实数
的值;
(2)求矩阵
的特征值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e7495ae0d9619e947469599314b6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e7c2faa5081b79fe03371644681b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f930a0cd9f13a80c9c299a8927a8496d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf488778044041cb085ae6104624a0e.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
(2)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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9 . 已知矩阵
的一个特征值是
,求矩阵
的另一个特征值
,及属于
的一个特征向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45ac21b2f642742ceaaf931f7415018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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10 . 已知二阶矩阵
有特征值
,其对应的一个特征向量为
,并且矩阵
对应的变换将点(1,2)变换成点(8,4),求矩阵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c9fde8d670b8d1bc619f5722467a87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb4c74e23acbd4b56f609036f37af65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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