题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215510-94313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215510-53610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215510-24121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215510-67247.png)
(Ⅰ) 数表
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215510-94313.png)
1 | 2 | 3 | ![]() |
![]() | 1 | 0 | 1 |
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215510-94313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215511-12237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215511-25375.png)
(Ⅲ)对由
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215510-53610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215510-24121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215510-67247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215510-94313.png)
能否经过有限次“操作”以后,使得到的数表每行的各数之
和与每列的各数之和均为非负整数?请说明理由.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215511-98889.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215512-75248.png)
解析
试题分析:(I)
法1:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215512-25352.png)
法2:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215512-47818.png)
法3:
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215513-78402.png)
(写出一种即可)
(II) 每一列所有数之和分别为2,0,
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215511-12192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215513-38070.png)
①如果操作第三列,则
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215513-41750.png)
则第一行之和为
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215513-12849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215514-86399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215514-58880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215514-78991.png)
②如果操作第一行
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215514-71502.png)
则每一列之和分别为
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215515-52918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215515-22078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215515-92621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215515-97964.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215512-75248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215512-75248.png)
(III) 证明:按要求对某行(或某列)操作一次时,则该行的行和(或该列的列和)
由负整数变为正整数,都会引起该行的行和(或该列的列和)增大,从而也就使得
数阵中
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215516-88139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215516-72742.png)
是改变数表中某行(或某列)各数的符号,而不改变其绝对值,显然,数表中
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215516-88139.png)
个数之和必然小于等于
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215516-27276.png)
之时必然所有的行和与所有的列和均为非负整数,故结论成立
点评:本题考查学生分析数据,总结、归纳数据规律的能力,关键是找出规律,要求学生要有一定的解题技巧.
核心考点
试题【设是由个实数组成的行列的数表,如果某一行(或某一列)各数之和为负数,则改变该行(或该列)中所有数的符号,称为一次“操作”. (Ⅰ) 数表如表所示,若经过两次“操】;主要考察你对等差数列等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215500-68793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215500-47897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215500-29341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215501-62406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215501-23003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215501-76109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215501-22386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215500-68793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215429-42642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215429-22393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215429-32217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215430-21248.png)
A.5 | B.6 | C.8 | D. 10 |
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215422-40129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215422-90233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215422-40129.png)
(Ⅰ)求通项
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215423-90130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215422-90233.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215423-56281.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215423-54194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215423-49405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215302-96748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215303-64083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215303-28852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215303-22222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215303-28852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215303-75732.png)
(1)求数列
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215302-96748.png)
(2)若S2为
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215304-75996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215304-78581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191009/20191009215219-54100.png)
A.1 | B.-1 | C.1 | D.0 |
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