名校
1 . 设2阶方矩阵
,则矩阵A所对应的矩阵变换为:
,其中
,
,其意义是把点
变换为点
,矩阵M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
,
的直线的方程;
(2)当变换矩阵
,点
经矩阵
的作用变换后得到点
,求实数m,n的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66226d08dd84a2e6dc096c3fcfc7e41c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc163fa0a2929ff019012aa3623088b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/909e45af90756a0dc1fee910b1661974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8061249592e9502a68f0d5b52172724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b08f646952c521d4f022af322b179a0a.png)
(1)当变换矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8b0cf31caa3e7c5c7dced1559726f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98ef6b26186130f8d88c66d3b3c78fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f87cae2228b72a1ec635860203496967.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5326817f9af012432a202749d1df59f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e210795a966bd5dc1293479ab1988b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5326817f9af012432a202749d1df59f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e210795a966bd5dc1293479ab1988b.png)
(2)当变换矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5184ca29a211cfb1c6b492993a608edd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/518dfce0a9aab04171383586c5077146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8fd27ebdd03bd80b1843c3f79e55ee.png)
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2 . 若矩阵
,定义
为行列式
的值,已知
,
,
,求矩阵
、
,并比较
和
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d08c396f1024c193297dfc269677636e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6561cc3fcdffc8bbf78c4e8fbad6e0cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/555eaed9ff42d175444d6c249e8c7bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354b2f69e6ed3a475d05a42958019c7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a95ef4c81a54df1906998a101d73a35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99de34d8d767424f869111af4cd2c538.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d134f3e5ccd2d58b567678256efc4de0.png)
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3 . 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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4 . 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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5 . 已知在直角坐标平面内,三角形
中
、
、
.
(1)求
边上的高所在直线的点法向式方程;
(2)求
的垂直平分线的点方向式方程;
(3)利用三阶行列式计算三角形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740c4190237d5fb6be669520cf9d685c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097e8a6a6de675f44d3bef88bb37375c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24dba5cc987db7f50f9b8e2d4544006d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)利用三阶行列式计算三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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6 . 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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7 . 已知
,
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3a1792c8a27289dcabe21bdee2b92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b5e7c5ff57bd768667cf19834ab0682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62d712f7ded863e7695e0133e15a15c.png)
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8 . 有这样一对矩阵
,
,通过计算发现
与
相等,即满足“
”.
请举出一对满足“
”要求的二阶矩阵
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d947e6a650c700ed1fab01b4b10fa6a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3722bda479c3d9229b99dc4f1c8fec71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93a42a8537d582e74cfac36d1d5f12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc166a17c8ce4b34134d13ac03f2005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9bee7a3e6a2c01e3196fd1dbe40cb4.png)
请举出一对满足“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9bee7a3e6a2c01e3196fd1dbe40cb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd82ec347d41082b344beb6dba4c6d2.png)
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9 . 已知矩阵
,
,
,求:
和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64275b96308af4f4539f669e95bdd496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec8aeb232f6f7112ffd618e01e535d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5855dc40a700ffab32e6a976c7a5c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f217f0146f6586844f73653849dd489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f65a03ad0f9172f992f42ae3bbb465e.png)
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10 . 已知
,
,
.
求(1)
;
(2)
;
(3)
;
(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92897241e445562143ff5189fda68779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae1fb5e85d42b55218f018a13b09d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c24d2ac3523c259705d29d4091cb33.png)
求(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ca74817b2425ef4f147246a98acdec.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2667f4762e93995b0bedff7a0b722f4e.png)
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