关于线性方程组一道易错题的注记  

A Note on a Fallible Problem of Linear Equations

作　　者：吴莺[1] 王湘君[1] WU Ying;WANG Xiangjun(School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China)

机构地区：[1]华中科技大学数学与统计学院,武汉430074

出　　处：《大学数学》2024年第6期81-85,共5页College Mathematics

摘　　要：由一道线性方程组的易错题,引发探讨存在矩阵B,使得BA=I成立与线性方程组AX=b是否有唯一的解的关系,其中A是任意矩阵,I是单位矩阵.进而,若BA=I成立,给出B的存在性和唯一性的充分必要条件,以及B的构造.同时,指出BA=I和AB=I能同时成立的充分必要条件.A mistake in a linear equation system led us to explore the relationship between the existence of matrix B,such that BA=I,and the unique solution of the linear equation system AX=b,where A is an arbitrary matrix and I is an identity matrix.Furthermore,for any matrix A we find sufficient and necessary condition for the existence and uniqueness of B,such that BA=I.And if matrix B exists,we construct B.We also point out the sufficient and necessary condition under which BA=I and AB=I can occur simultaneously.

关 键 词：线性方程组 解 集合 矩阵相乘 单位矩阵 秩 

分 类 号：O151.2[理学—数学]