名校
1 . 已知a,b,c,d∈R,矩阵A=
的逆矩阵A-1=
.若曲线C在矩阵A对应的变换作用下得到直线y=2x+1,求曲线C的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3724503b27f41015a970524b96d2c9b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/206cbe350fef3f4dd8f4b0ee7876c2a4.png)
您最近一年使用:0次
2020-02-25更新
|
126次组卷
|
4卷引用:【市级联考】江苏省七市(南通、泰州、扬州、徐州、淮安、宿迁、连云港)2019届高三第三次调研考试数学试题含附加题
2 . 已知曲线C:x2+2xy+2y2=1,矩阵A=
所对应的变换T把曲线C变成曲线C1,求曲线C1的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f5e60de441946de25eec2711ef14cf5.png)
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3 . 已知矩阵M=
的一个特征值为λ=3,其对应的一个特征向量为α=
,求直线l1:x+2y+1=0在矩阵M对应的变换作用下得到的曲线l2的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d52ff9212528af8bf42241f0f4bc9df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fcac75bd925aec6c58d030b45aa4ba0.png)
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解题方法
4 . 将曲线xy=1绕坐标原点按逆时针方向旋转45°,所得曲线的方程为______ .
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5 . 定义
为向量
到向量
的一个矩阵变换,设向量
为坐标原点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a7c1e2c35812a602502841ed6c402b3.png)
_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0df4654f75c155ddce56936fc73d82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4555aaa044fa3370a55f208f8361e787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b257c5e82589ea530dc7e2b5a8d1bd20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ab10bbdafdae8e04bc246ca2cf413d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a7c1e2c35812a602502841ed6c402b3.png)
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18-19高二上·上海浦东新·阶段练习
名校
6 . 设二阶方矩阵
,则矩阵
所对应的矩阵变换为:
,其意义是把点
变换为点
,矩阵
叫做变换矩阵.
(1)当变换矩阵
时,点
、
经矩阵变换后得到点分别是
、
,求经过点
、
的直线的点方向式方程;
(2)当变换矩阵
时,若直线上的任意点
经矩阵变换后得到的点
仍在该直线上,求直线的方程;
(3)若点
经过矩阵
变换后得到点
,且
与
关于直线
对称,求变换矩阵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a72b9c5c237f830cf302e780c8a65ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc163fa0a2929ff019012aa3623088b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ead0c5a16ce4734c9e60838f927e894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)当变换矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103cac0a1fed34ab690764afa75a1bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79fef5c2bdeab99d9d397c2dce4b416d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90b747a0d6458d973963bce3606eb74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
(2)当变换矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e5794bde4de317a991f4e48650eb25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
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名校
7 . 已知矩阵
(
)满足
(I为单位矩阵).
(1)求m的值;
(2)设
,
.矩阵变换
可以将点P变换为点Q.当点P在直线
上移动时,求经过矩阵A变换后点Q的轨迹方程.
(3)是否存在这样的直线:它上面的任一点经上述变换后得到的点仍在该直线上?若存在,求出所有这样的直线;若不存在,则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ae8916e1faea682be8638014206f1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc5b5b4e907101a09814f3a875a2370.png)
(1)求m的值;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1481b5b0bb2eb2481ae11141a2fdae87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0413d6be96193ce48787639ef2c669a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06553b7e77205d053c1981e9c050d579.png)
(3)是否存在这样的直线:它上面的任一点经上述变换后得到的点仍在该直线上?若存在,求出所有这样的直线;若不存在,则说明理由.
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8 . 关于
的矩阵
,列向量
.
(1)已知
,
,
,计算
,并指出该算式表示的意义;
(2)把反比例函数
的图象绕坐标原点逆时针旋转
,求得到曲线的方程;
(3)已知数列
,
,猜想并计算
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e16fcd8304a0a925d12b19f829ffdef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/777b1de5c57f879215e1cca147a76820.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e4fd085ee10f340a008389c4a1a80d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7656966dffb3078f7298e3c5cb7a3d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f8bf4795ad38b3417ab4e5499df2bf.png)
(2)把反比例函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377a2333ff8c63cbdb20b882d6d5a7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a78a26e3eeac053424c52ab90f6a3490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa694d7b39bd011907d735372ba6874.png)
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名校
9 . 线性方程组
的增广矩阵是________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33477f3e435d54c57aae4ba05a297da7.png)
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10 . 已知矩阵
.
(1)求
;
(2)若曲线
在矩阵
对应的变换作用下得到另一曲线
,求
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ad0004771df5fef239fdb4e219229d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5281a7e4f6d37e698366c83fa38d7b6a.png)
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca83a3c2edc7a1d19930fc2dea18b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2019-09-26更新
|
138次组卷
|
2卷引用:江苏扬州高邮市2019-2020高三上学期开学考试数学(理)试题