1 . 如图一,在平面直角坐标系
中,
为坐标原点,
,
,请根据以下信息,处理问题(1)和(2).信息一:
为坐标原点,
,若将
顺时针旋转
得到向量
,则
,且
;信息二:
与
的夹角记为
,
与
的夹角记为
,则
;信息三:
;信息四:
,叫二阶行列式.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/bf1df5da-7d9c-4f37-97ec-8360f768f8bf.png?resizew=306)
(1)求证:
,(外层“
”表示取绝对值);
(2)如图二,已知三点
,
,
,试用(1)中的结论求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47d5a819f2e82edbac8a82b05f64501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effc7768e61293768fcaf8c8979ff109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b9cffa9e859c54c97c1d58749f1993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36be470b9902a88939057d2f55280e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47d5a819f2e82edbac8a82b05f64501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774e4c61b6568d292d5bc576d3310d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b9cffa9e859c54c97c1d58749f1993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774e4c61b6568d292d5bc576d3310d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad852a240fd16f5430472a3ff8c4063c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98afd2734ffaecbcb49e17416de7f062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d81a1c2ae937c87ee40f6b5d3e06bee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/bf1df5da-7d9c-4f37-97ec-8360f768f8bf.png?resizew=306)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14e7b25d10dbe02750492faf9d0cd96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd483afbcdcd303e0c66ab48838bedfc.png)
(2)如图二,已知三点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773c2dd14d50e7f0d3326af4833d899a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5249114b149be585bc9b0fa1ae77e4ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed283a253b61df01f2a1cdc0cd8003f3.png)
您最近一年使用:0次
2020-08-03更新
|
218次组卷
|
2卷引用:贵州省贵阳市2019-2020学年高一下学期期末考试数学试题
2 . (1)阅读下列材料并填空:对于二元一次方程组
,我们可以将
、
的系数和相应的常数项排成一个数表
,求得的一次方程组的解
,用数表可表示为
.用数表可以简化表达解一次方程组的过程如下,请补全其中的空白:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fa4b5235bb10623608919e64bd24cf.png)
,从而得到该方程组的解集________ ;
(2)仿照(1)中数表的书写格式写出解方程组
的过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864fcfc0d004b4daaa98eb2b525d931c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e59a3f06077857c62cef6fb2ee5200f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48934fc87ea424eb321d89807eee5ae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c639bddf78c5ae53dc9920c35290013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fa4b5235bb10623608919e64bd24cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bbc2489fd47fa0a234cd6af540746e.png)
(2)仿照(1)中数表的书写格式写出解方程组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a82d7108a93b94eb934071e27155113c.png)
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3 . 已知
=
是矩阵M=
属于特征值λ1=2的一个特征向量.
(Ⅰ)求矩阵M;
(Ⅱ)若
,求M10a.
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908679688192/1571908685438976/STEM/36af06dc9e6b45658ac244111813be00.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908679688192/1571908685438976/STEM/cbc01f7080bf452297948908a4bd8079.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908679688192/1571908685438976/STEM/491d4d91de984a94990224df77d37d42.png)
(Ⅰ)求矩阵M;
(Ⅱ)若
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908679688192/1571908685438976/STEM/c18bee516d374a4abfac5e0ca18607f2.png)
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13-14高一·全国·课后作业
4 . 已知矩阵A=
,向量
=
.求向量
,使得A2
=
.
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908478935040/1571908484694016/STEM/a8d5ec7e5b8443d792b12f73c3586926.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908478935040/1571908484694016/STEM/510be974f37643128ce60275d893846e.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908478935040/1571908484694016/STEM/7aac76233bc44a9d939fcd01bfa78ac4.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908478935040/1571908484694016/STEM/6c34684172be446494ad6d05bcdab1ea.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908478935040/1571908484694016/STEM/6c34684172be446494ad6d05bcdab1ea.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908478935040/1571908484694016/STEM/510be974f37643128ce60275d893846e.png)
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