1 . 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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2019-11-08更新
|
288次组卷
|
7卷引用:上海市虹口区上海外国语大学附属外国语学校2019-2020学年高二上学期期末数学试题
名校
2 . 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: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
3 . 已如变换
对应的变换矩阵是
,变换
对应的变换矩阵是
.
(Ⅰ)若直线
先经过变换
,再经过变换
后所得曲线为
,求曲线
的方程;
(Ⅱ)求矩阵
的特征值与特征向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cc8019ddbc7d76db6058397c2e19d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b58f796d6d58fa53a8215017205846.png)
(Ⅰ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c1212804e6d784756d48083d166e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9089c8427b51b9fad79f311938190b4.png)
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4 . 已知矩阵
,矩阵B的逆矩阵
.
(1)求矩阵A的特征值及矩阵B.
(2)若先对曲线
实施矩阵A对应的变换,再作矩阵B对应的变换,试用一个矩阵来表示这两次变换,并求变换后的结果.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27808e342b2864b11b838ba7f95b632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08876f55ffc5c720564e8e0cba17ce66.png)
(1)求矩阵A的特征值及矩阵B.
(2)若先对曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
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5 . 已知矩阵
.
(1)求
;
(2)求矩阵
的特征值和特征向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8f0737d7694eeda54d3207819f1785f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a335fc7c2c46946f0bf908c78bcc46fa.png)
(2)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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6 . 已知点
在矩阵
对应的变换作用下得到的点
,求:
(1)矩阵
;
(2)矩阵
的特征值及对应的特征向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f5280c221f33c454f6174e0af875ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0788b20df56c530aa535f50adf1332.png)
(1)矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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7 . 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
|
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
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 . 已知矩阵A=
,向量
.
(1)求A的特征值
、
和特征向量
、
;
(2)求A5
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7bfb6d45311dc703a09c825b4f190b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9f80f530eb9de37ccc8482a1423e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12318ffc990d4be8ccf3842e0beb1fd3.png)
(1)求A的特征值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5dc876d7dcd3c971b36d26668b1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7345f310975ddb40dca94b5135c35dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b765718479c160ba61ec5c6f8c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e29bf5652f0d4f764c3606efcdb445f.png)
(2)求A5
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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2018-06-30更新
|
268次组卷
|
2卷引用:【全国市级联考】江苏省宿迁市2017~2018学年第二学期高二数学(理)试题
10 . 已知矩阵
,向量
.
(1)求
的特征值
、
和特征向量
、
;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21079bf90a520b73444fbfa5a84dd4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb7012bd763528e444b94d9e90ac004.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5dc876d7dcd3c971b36d26668b1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7345f310975ddb40dca94b5135c35dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b61c0f79028b8d728408d131e917f3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb301ef8b2be62628dc1378f3168630f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68555568c030eb425271141b6511ce89.png)
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