1 . 求使等式
成立的矩阵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e1869f664247e1f5dd66515a9857e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2 . 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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3 . 已知矩阵
,若矩阵
属于特征值3的一个特征向量为
,属于特征值-1的一个特征向量为
,求矩阵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/600e41c24f132528151a1588cfbd7da1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034bb3402926a68011b053ef16d8c83b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561e6b6f8b149a2aac713047de67478d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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4 . 已知矩阵
,
,直线
经矩阵
所对应的变换得到直线
,直线
又经矩阵
所对应的变换得到直线
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71c82422af9bb7bad3a29bbab0915a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1efd5ca628e39905068e0045600a5e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21b48a99b6c3582a0e62e164430e81e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb37c3caee98909bce78d6dd51ffb4f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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5 . 若一个变换所对应的矩阵是
,求抛物线
在这个变换下所得到的曲线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/514b8d2c2a2c938d4cfa96f08d1d4719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5545195ade2bda359e683715332e83.png)
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6 . 已知
,
是实数,如果矩阵
所对应的变换
把点
变成点
.
(1)求
,
的值.
(2)若矩阵
的逆矩阵为
,求
.
![](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/64468f95518d1de84db21d05f2233a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3654254401fc902c3cb4912969f21f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad42625f296d2a4b65180e2f7b776beb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若矩阵
![](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/f6cb94d93b169adeffd262c1667257a0.png)
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7 . 曲线
在矩阵
的作用下变换为曲线
,求
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f6d926590ae5d35e8a6123074413e3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69085f74c23f1152b5f0a1bb19acd362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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8 . 求出曲线
依次经过矩阵
,
作用下变换得到的曲线方程
,求实数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58baa1501e3502998a10756803ffa24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f9c14a3e83c8236136680e83dda816a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f4123c19136d3a4dc040dce8e34e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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9 . 已知矩阵
,B=![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f396288a90994415e92cd47dd2a3401.png)
(1) 求AB;
(2) 若曲线C1:
在矩阵AB对应的变换作用下得到另一曲线C2,求C2的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e401acac9c4ec799b35bfad6fa467ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f396288a90994415e92cd47dd2a3401.png)
(1) 求AB;
(2) 若曲线C1:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e4a41cbe3d1f25154602dee11d36ee.png)
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10 . 已知矩阵M=
,向量β=
,求M4β.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c382640c2fa1d4850995ea4b923025e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aacb971fb70e3200e8054892960b7ee.png)
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