线性代数中向量组的线性表示、极大无关组及线性方程组快速求解  

Linear Representation of Vector Group,Quick Solutions to Maximal Independent Group and Linear Equations in Linear Algebra

作　　者：晏建学[1] 王云秋 Yan Jianxue;Wang Yunqiu(School of Business,Yunnan University of Finance and Economics,Kunming Yunnan 650221,China;School of Statistics and Mathematics,Yunnan University of Finance and Economics,Kunming Yunnan 650221,China)

机构地区：[1]云南财经大学商学院,云南昆明650221 [2]云南财经大学统计与数学学院,云南昆明650221

出　　处：《曲靖师范学院学报》2018年第6期17-21,共5页Journal of Qujing Normal University

摘　　要：通过对线性代数中"向量与向量组的线性表示、向量组的极大无关组及线性方程组求解"过程加以改进,将传统的"对列向量构成的矩阵或线性方程组增广矩阵(1)用行初等变换化成阶梯形;(2)再用初等行变换化成行简化阶梯形"的两步求解过程简化为"对列向量构成的矩阵转置或线性方程组增广矩阵转置(1)用行初等变换化成阶梯形"一步求解,不仅节约了一定的工作量,还有效地降低了求解难度.In this paper, the two - step solution process is simplified to the one - step process, in which the transpose matrix of column vectors or the transpose augmented matrix of linear equations are transformed into a ladder by the means of elementary row transformation. The improvement not only reduces a certain amount of the workload but also lowers the difficulty of seeking solutions.

关 键 词：向量组 极大无关组 线性方程组 矩阵 转置 初等行变换 阶梯形 行简化阶梯形 

分 类 号：O151.2[理学—数学]