1 . 已知
,
,若点
在矩阵
对应的变换作用下得到点
,求矩阵
的逆矩阵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10570c017a8e9ced002591abf78bc2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1cfae3eb175e5e6103ae0264749a44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd10eee59091bfbdd211a2e599e7aecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fada029ae6bfffbcef1ba68f1bec9b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c274643da306d2adb6f9b4e8dc5ff105.png)
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2 . B.选修4—2:矩阵与变换
设二阶矩阵A=
.
(Ⅰ)求A-1;
(Ⅱ)若曲线C在矩阵A对应的变换作用下得到曲线C:6x2-y2=1,求曲线C的方程.
设二阶矩阵A=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b4360d65302210b195370e5b6ae913.png)
(Ⅰ)求A-1;
(Ⅱ)若曲线C在矩阵A对应的变换作用下得到曲线C:6x2-y2=1,求曲线C的方程.
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13-14高三下·江苏盐城·开学考试
3 . 已知矩阵
,
(1)求逆矩阵
;(2)若矩阵
满足
,试求矩阵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2192e8ca9aa94cc6d96e4d389559ff83.png)
(1)求逆矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a84646168f0afc4380043a52b818c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4466c31731e3ba4b6004316a58f199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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4 . 已知矩阵
,若矩阵
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
,并写出
的逆矩阵.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f02ff81e67540f3786ef925627c27b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034bb3402926a68011b053ef16d8c83b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1120b0db61007dcfc2258ef63e1021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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5 . 已知矩阵
的一个特征值
及对应的特征向量
.求矩阵
的逆矩阵.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d53a956d7d0e4596a9b4a95da6355a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4712ae924da953c4451dd78b8d6ac2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86381a1bdfd8dcf51621b00215f2ffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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6 . 已知矩阵
的一个特征值
所对应的一个特征向量
,求矩阵
的逆矩阵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6aed1ab182d107a68dc6f2d1a932cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfec4233214c3a729c843dee0d186db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b652ec145d1eaf9a72ce4f532004ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a84646168f0afc4380043a52b818c35.png)
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7 . 若矩阵
,
,求矩阵
的逆矩阵.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08bdb5fc25f83a62f6fd0d127a010410.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd378ddb75ce1bc9acb30ba1c2154796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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8 . 已知
,向量
是矩阵
的属于特征值
的一个特征向量,求
与
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e779eb737f6f85b25e411903a10ee814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2665433f4931d76f2fcaa6739f5d5ac5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1bd71c95094b5f46fc0b50f781aa74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a84646168f0afc4380043a52b818c35.png)
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9 . 已知矩阵
的一个特征值为
,其对应的特征向量为
,求矩阵A的逆矩阵.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d96b681025cc1227b79976a347e2ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05df47d88bb64fe00c6ef3b9b3699617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6750777a85cfcff45fa7c56e064f101.png)
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