1 . 已知二阶矩阵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d143375802993bd449e0d7c0a18936b.png)
,若矩阵
属于特征值
的一个特征向量
,属于特征值3的一个特征向量
.
(Ⅰ)求实数
的值;
(Ⅱ)若向量
,计算
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d143375802993bd449e0d7c0a18936b.png)
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572071209197568/1572071215439872/STEM/6e9b0de22e2243a9afb80d50343ed543.png)
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572071209197568/1572071215439872/STEM/361506345301453ebb568296d2a78a2e.png)
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572071209197568/1572071215439872/STEM/6e40527a9dab4fc9ba5168f0559ca978.png)
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572071209197568/1572071215439872/STEM/8f64b23d9d07413d8942fbce1131e9a7.png)
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572071209197568/1572071215439872/STEM/4fe7f9f17f2c47cc8be6c3e81d12d652.png)
(Ⅰ)求实数
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572071209197568/1572071215439872/STEM/039ad277b84a41c4ad0fadbd9bb6b700.png)
(Ⅱ)若向量
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572071209197568/1572071215439872/STEM/302560e34fe1444194e5362c87f389fa.png)
![](https://img.xkw.com/dksih/QBM/2015/4/15/1572071209197568/1572071215439872/STEM/56ac6faea43c43bb92056ab41cf957e5.png)
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2 . 选修4-2:矩阵与变换
已知二阶矩阵
有特征值λ1=4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-1的一个特征向量
, ![](https://img.xkw.com/dksih/QBM/2015/4/13/1572066045181952/1572066051293184/STEM/0bef74b25a1f46619b105241348f4bc6.png)
(Ⅰ )求矩阵
;(Ⅱ )求
.
已知二阶矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/2015/4/13/1572066045181952/1572066051293184/STEM/ee26bfafa7b44d24a6a83d17c7aa1a6e.png)
![](https://img.xkw.com/dksih/QBM/2015/4/13/1572066045181952/1572066051293184/STEM/114c3e71eef4455fae4d2868d3849891.png)
![](https://img.xkw.com/dksih/QBM/2015/4/13/1572066045181952/1572066051293184/STEM/3e454d2b58004191991f44323e79a5fc.png)
![](https://img.xkw.com/dksih/QBM/2015/4/13/1572066045181952/1572066051293184/STEM/0bef74b25a1f46619b105241348f4bc6.png)
(Ⅰ )求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1bb74c828afd6441d6ff6b1975f211.png)
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3 . 已知矩阵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167b6b68086219d6e1211789a8a69878.png)
.
(1) 求
的逆矩阵
;
(2)求矩阵
的特征值
、
和对应的特征向量
、
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167b6b68086219d6e1211789a8a69878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da97c523361b2a525b640d389d3d7cbe.png)
(1) 求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5d7c1beea03e1dd6f5a0e12ea2b7585.png)
(2)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272253d491aed8f9faa751aee7dbbb98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01809949e4829653548ca64dffbe06b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b4ea25518db7db48cfdd846260d82a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25bbe7456710281aabf89ea879e69a31.png)
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真题
4 . 已知矩阵A的逆矩阵
,求矩阵A的特征值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7da97b363bfda2e80c1b987cab2349.png)
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5 . (1).选修4-2:矩阵与变换
已知矩阵
,向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14093f7f8cb43fdf9c6210ea2f9f3806.png)
(I)求矩阵
的特征值
、
和特征向量
、
;
(Ⅱ)求
的值.
已知矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bdc1eb049a5342424639e420fc168d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14093f7f8cb43fdf9c6210ea2f9f3806.png)
(I)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5dc876d7dcd3c971b36d26668b1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7345f310975ddb40dca94b5135c35dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b765718479c160ba61ec5c6f8c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e29bf5652f0d4f764c3606efcdb445f.png)
(Ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68555568c030eb425271141b6511ce89.png)
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6 . 已知矩阵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870893d94230820d6b673794225e2578.png)
,A的一个特征值
,其对应的特征向量是
.
(Ⅰ)求矩阵
;
(Ⅱ)求直线
在矩阵M所对应的线性变换下的像的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870893d94230820d6b673794225e2578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0242a562dd4410ada8af4fa0cd75575a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2f2d7c81cb44416bcdf59419637682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e21bf558d9bdcaafb7c12d21d4c4ac5.png)
(Ⅰ)求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
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