线性方程组可解条件在一个初等数学问题中的应用  

Application of the existence condition of solution of linear equations to an elementary mathematical problem

作　　者：李静[1] 徐为[1] LI Jing XU Wei(School of Science, PLA University of Science and Technology, Nanjing 211101, China)

机构地区：[1]解放军理工大学理学院,江苏南京211101

出　　处：《高师理科学刊》2017年第9期11-13,共3页Journal of Science of Teachers＇College and University

基　　金：解放军理工大学校级教育教学课题(GJ1507038)

摘　　要：讨论了一个关于在正方形中截取矩形的初等数学问题,通过建模把问题转化成判断一个线性方程组是否有解的问题,由于系数矩阵的秩小于增广矩阵的秩,因而线性方程组无解,从而原截取矩形问题无解.The problem of cutting rectangles from an square is discussed, it is formulated as a problem of whether a set of linear equations is solvable or not through constucting mathmatical model. Straight judging forward calculation shows that the rank of the coefficient matrix is smaller than the augmented matrix, which means that the set of equations is not solvable. Thus, the problem of concern is not solvable.

关 键 词：矩阵 线性方程组 秩 可解条件 

分 类 号：O151.26[理学—数学]