1 . 已知
,向量
是矩阵
的属性特征值
的一个特征向量,矩阵
以及它的另一个特征值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64541d7f445079207b6f671adc7d662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0b102eb6846393c0a635d0317953050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da359be334fd24f02a3571f3c04bccc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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真题
2 . A.选修4 - 1:几何证明选讲
如图,在四边形ABCD中,△ABC≌△BAD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/2fb8b93f-94db-4268-8eb7-7406b5fa70c1.png?resizew=150)
求证:AB∥CD.
B.选修4 - 2:矩阵与变换
求矩阵
的逆矩阵.
C.选修4 - 4:坐标系与参数方程
已知曲线C的参数方程为
(
为参数,
),求曲线C的普通方程.
D.选修4 - 5:不等式选讲
设
≥
>0,求证:
≥
.
如图,在四边形ABCD中,△ABC≌△BAD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/2fb8b93f-94db-4268-8eb7-7406b5fa70c1.png?resizew=150)
求证:AB∥CD.
B.选修4 - 2:矩阵与变换
求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa537c9a8b597c99e7fc6165843593b.png)
C.选修4 - 4:坐标系与参数方程
已知曲线C的参数方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624ae69d616d8118c4e196d5658f4e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
D.选修4 - 5:不等式选讲
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d318a788e491a9169b56ba90cf4dbe7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662c2bb1fdc296fcd2effd0a9b45fe06.png)
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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
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6卷引用:江苏省南京市江宁区2018-2019学年高二第二学期期末学情调研卷数学试题
4 . 行列式
中,6的代数余子式的值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af39283d10056a7a74d0eb923f4c0a8e.png)
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7卷引用:上海市控江中学2018-2019学年高二上学期期中质量调研数学试题
5 . 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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|
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3卷引用:【市级联考】江苏省扬州市2019届高三第一学期期末检测数学试题
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 . 选修4—2:矩阵与变换已知矩阵
的逆矩阵
.
(I)求矩阵
;
(II)求矩阵
的特征值以及属于每个特征值的一个特征向量.
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327182180352/1578327182835712/STEM/f6d63eba83df472b9e01f80e2a5881c0.png)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327182180352/1578327182835712/STEM/daf3b311d33545e1aa3786cb22ace5ec.png)
(I)求矩阵
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327182180352/1578327182835712/STEM/f6d63eba83df472b9e01f80e2a5881c0.png)
(II)求矩阵
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327182180352/1578327182835712/STEM/b9e1bca386ac46df84eaedb5d188b562.png)
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8 . (1)已知矩阵
的一个特征值为
,其对应的特征向量
,求矩阵
及它的另一个特征值.
(2)在极坐标系中,设P为曲线C:
上任意一点,求点P到直线l:
的最小距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde3466fd11acc1467114f8bd6c054c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05df47d88bb64fe00c6ef3b9b3699617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a58eacc2e14a83d0524c1a2bf152a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)在极坐标系中,设P为曲线C:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f917a2022014d9c19c29eeac84c74e2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97eb513bf853ea7602fee1850bbc1cb.png)
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9 . 已知
,
是矩阵
的一个特征向量,求
的逆矩阵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce55304240e6d1ccd4240145816435df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11585b5dfac3626665974fdbddce25ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfcaeccb9f62416994eed14d82b5ba5.png)
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2020-06-04更新
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2卷引用:2020届江苏省七市(南通、泰州、扬州、徐州、淮安、连云港、宿迁)高三下学期第三次调研考试数学试题
10-11高三下·江苏扬州·期末
名校
10 . B.选修4—2 矩阵与变换
已知矩阵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
,其中
,若点
在矩阵
的变换下得到点
,
(1)求实数a的值;
(2)求矩阵
的特征值及其对应的特征向量.
已知矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99cb445bb4dd025a31a94859cdbb6ff4.png)
![](https://img.xkw.com/dksih/QBM/2011/5/4/1570137103917056/1570137109594112/STEM/6d4d9d4934284ae4ba209a3acfea7402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5631beb2a5954e3abf3b206d9e5ea0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aba6509b9dcf47721653e2cf5c8de71.png)
(1)求实数a的值;
(2)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2018-03-02更新
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5卷引用:2011届江苏省扬州中学高三下学期期末考试数学试卷
(已下线)2011届江苏省扬州中学高三下学期期末考试数学试卷(已下线)2011届江苏省南京六中高三下学期期中考试理数江苏省盐城中学2018届高三上学期期末考试数学试题2【全国百强校】江苏省泰州中学2017-2018学年高二6月月考数学(理)试题【市级联考】江苏省徐州市2019届高三12月月考数学试题