1 . 在平面直角坐标系中,矩阵
对应的变换将平面上的任意一点
变换为点
.
(Ⅰ)求矩阵
的逆矩阵
;
(Ⅱ)求圆
在矩阵
对应的变换作用后得到的曲线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc76f77480174835ec2689e01d48e73a.png)
(Ⅰ)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5281a7e4f6d37e698366c83fa38d7b6a.png)
(Ⅱ)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2 . 已知矩阵
.
(1)求A的逆矩阵
;
(2)求矩阵C,使得AC=B.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b43edc537cdde40ae44130add6bf43.png)
(1)求A的逆矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c274643da306d2adb6f9b4e8dc5ff105.png)
(2)求矩阵C,使得AC=B.
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3 . 选修4-2:矩阵与变换
已知矩阵
.
(1)矩阵
对应的变换把直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
变为直线
,求直线
的方程;
(2)求
的逆矩阵
.
已知矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3950ec85f2dad873553b2a3e839d6686.png)
(1)矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3950ec85f2dad873553b2a3e839d6686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1a686b80b8f109a929f58c2de7201d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fd522fff2452469a48916de2535dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fd522fff2452469a48916de2535dc1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa5694373bd78b1ca2180f831bf1c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a4d1d38989ee6434e43bed98c5c19d.png)
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10-11高三·福建泉州·阶段练习
解题方法
4 . (1)(矩阵与变换)已知二阶矩阵
.
①求矩阵
的逆矩阵;
②设向量
,求
.
(2)(坐标系与参数方程)
已知曲线
的参数方程为
(
是参数),曲线
的极坐标方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d57678b93f1dcb18d4cbb33ff70bce0.png)
.
①求曲线
的普通方程和曲线
的平面直角坐标方程
②设曲线
和曲线
相交于
、
两点,求弦长
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fc8684e2254e54a0e013b38da9f85d.png)
①求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
②设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3ef826de1c83db4ed893c6175abcd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec30caa146cf636a9bf7aadbb381c4c.png)
(2)(坐标系与参数方程)
已知曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb06061053b1d79e76431bfdbcb0d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d57678b93f1dcb18d4cbb33ff70bce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2fefd4562c09c2f5afbb3987149fcd.png)
①求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
②设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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10-11高二下·福建泉州·期末
5 . 已知矩阵
,A的一个特征值
,属于λ的特征向量是
,求矩阵A与其逆矩阵.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c218267974a6ba1d84042c5ae363ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2f2d7c81cb44416bcdf59419637682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6d759d2e7b128d67f3c00b584bc9a5.png)
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6 . 设矩阵
(其中
).
(1)若
,求矩阵M的逆矩阵
;
(2)若曲线C:
在矩阵M所对应的线性变换作用下得到曲线
:
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f5c986bef596a4400e3bc7d40cafe61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67784e0c5b774a658b3c12fe05800df.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c81d900f8e024ca73659cabac53e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5281a7e4f6d37e698366c83fa38d7b6a.png)
(2)若曲线C:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
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