1 . 已知矩阵
的一个特征值为
,向量
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae206edf2287a206ba6c5e7b93d7daff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed127ce2b4a6fc3573fb0a6bc4664aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13fb1e34c85baa2279c12c88b8b7b99.png)
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2 . 已知二阶矩阵M有特征值
及属于特征值4的一个特征向量
并有特征值
及属于特征值
的一个特征向量
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5c54cac499eca63b317a7a82872351.png)
(1)求矩阵M;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645f7ad14b3bc8e25e66a6db2e67a3b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb2adbeb3c989a133f18542ad04d905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c300b4cce8a3cd83e81ec46c2a75165b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d596913e7356226332a9d9d1dea81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5c54cac499eca63b317a7a82872351.png)
(1)求矩阵M;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd6c505e4e0f9f2c89a5672c6dd1b555.png)
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3 . 已知矩阵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d8c1a4077bee8d516b4964000582d6e.png)
(1)求矩阵
的逆矩阵;
(2)求该矩阵的特征值和特征向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d8c1a4077bee8d516b4964000582d6e.png)
(1)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)求该矩阵的特征值和特征向量.
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4 . 已知矩阵
的一个特征值为2,其对应的一个特征向量为
.
(1)求矩阵A;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d8c82801f23fd1c407b3f0635183bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0920368ba6bf1a80cd0ffeb5aadf38a.png)
(1)求矩阵A;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56f7dda48336b4051c633b4ee85cf20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
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5 . 已知矩阵
,点
在矩阵
对应的变换作用下变为点
.
(1)求
,
的值;
(2)求矩阵
的特征值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6946bbc978269872c0cbbc659a3070d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d25e70d37af93796965efc8d342185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6fe915da51b1be6414ac2b92b3cea5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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2020-07-15更新
|
88次组卷
|
3卷引用:江苏省徐州市2020届高三下学期考前模拟(四模)数学试题
6 . 已知矩阵M=
β=
,计算M6β.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c382640c2fa1d4850995ea4b923025e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12df68055572f9b065c5be7d0f2791be.png)
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7 . 已知矩阵
,求矩阵
的逆矩阵
的特征值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9736bd17c98edd2fa22286838e7ef51a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a84646168f0afc4380043a52b818c35.png)
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8 . 已知二阶矩阵
的特征值是
所对应的一个特征向量
.
(1)求矩阵
;
(2)设曲线
在变换矩阵
作用下得到的曲线
的方程为
,求曲线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41c0fee0e838e21a54f1670272cc20a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c9c39efc53af82fec6d9cf76db5afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3931901314aed7839c378dd6386d8da.png)
(1)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3557809c066e68395b614535a7675e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377a2333ff8c63cbdb20b882d6d5a7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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9 . 求矩阵
的特征值及对应的特征向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c20a6d35ce9169e9dcd34b43512e5f.png)
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10 . 已知点M(2,1)在矩阵A=
对应的变换作用下得到点N(5,6),求矩阵A的特征值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2732231b2ee95a4a326bf8412649e8fa.png)
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