名校
解题方法
1 . 我们学过二维的平面向量,其坐标为
,那么对于
维向量,其坐标为
.设
维向量的所有向量组成集合
.当
时,称为
的“特征向量”,如
的“特征向量”有
,
,
,
.设
和
为
的“特征向量”, 定义
.
(1)若
,
,且
,
,计算
,
的值;
(2)设
且
中向量均为
的“特征向量”,且满足:
,
,当
时,
为奇数;当
时,
为偶数.求集合
中元素个数的最大值;
(3)设
,且
中向量均为
的“特征向量”,且满足:
,
,且
时,
.写出一个集合
,使其元素最多,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1be0a1f60498f041589dccfb67c3bbde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50faa5111383084d53ee8a26434a617b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d483285e0e25aa74c75d3368dd6205bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50faa5111383084d53ee8a26434a617b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576a174f70ea49c333046a7e1ec62d92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49fe7103cc7ee651e8439a55c2a309e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/962848ecd2c3e636df8574d3e5348ffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d935c381da3d9373c2147d25dd07714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71d1197f0849725db71c29c0eaf7561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eee8f3d77056e708ed29290fc314d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3899fa225ad8f95f8d4d448808becebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b36b33e38fb99947ad5cecf0e86cf2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574dd4734831662d4d4cf2f8fda97632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7741a2d39d8f0b1cc77af746efe629d0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8abaee1c69773edf2ab23813457e7133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbd4f6dbf1c8a007f453adbe4736a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe90b06814f2067a471cffa639fd235a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b79675934e436ed9788ea0d3fde6c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2563777fd5675f04e4abe4331899241f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cd69465b3cd5e5493b763ef83caa3b.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e5108b9554f792cf2983ba3389b9ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8acd9af497a2f40eb407d47476f0f4cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4336fe2e523f296e762fb4f3968a5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdca1393b642fbc6784de187fceef56c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cd69465b3cd5e5493b763ef83caa3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38ea10e8fca3e7c46d57d3720457bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cd69465b3cd5e5493b763ef83caa3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56143137af67c65ae0feca9ec96c89f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8acd9af497a2f40eb407d47476f0f4cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4336fe2e523f296e762fb4f3968a5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38ea10e8fca3e7c46d57d3720457bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4363cb382c4f87ab555045a11db7c5c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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2021-09-06更新
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4卷引用:北京市一零一中学2020-2021学年高一下学期期中考试数学试题