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令人瞩目的2012年高考落下帷幕.数学考题林林总总,异彩纷呈,令人目不暇接.其中北京卷理科第20题选材平实但立意深远,对考生来说背景公平,但考查了学生的数学素养和理性思维能力.本文对第三问的解决策略作浅显的探求,对其一般性作适当的推广.题目是这样的:设A是由m×n个实数组成的m行n列的数表,满足:每个数的绝对值不大于1,且所有数的和为零.记S(m,n)为所有这样的数表构成的集合.
Highlights of the 2012 college entrance examination came to an end.Mathematical questions are everywhere, colorful, dizzying.The Beijing Volume 20 subjects of science subjects, but far-reaching imaginative candidates for the background fair, but examining the students’ mathematical qualities and rationality Thinking ability.This article on the third question to solve the strategy to make a brief exploration of its generality for the appropriate promotion.The title is this: Let A is a m × n real number composed of m rows and n columns of the number of tables to meet : The absolute value of each number is not greater than 1, and the sum of all the numbers is 0. Note that S (m, n) is a collection of all such tables.