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线性方程组的增广矩阵经初等变换变为,则当λ=(  )时方程组AX()b()有解。

发布日期:2021-08-30

线性方程组的增广矩阵经初等变换变为,则当λ=(  )时方程组AX(→)=b(→)有解。
A

λ=0

B

λ≠1

C

λ≠2

D

λ≠0且λ≠1

试题解析

线性方程组

线性方程组是各个方程关于未知量均为一次的方程组(例如2元1次方程组)。对线性方程组的研究,中国比欧洲至少早1500年,记载在公元初《九章算术》方程章中。线性方程组有广泛应用,熟知的线性规划问题即讨论对解有一定约束条件的线性方程组问题。

中文名
线性方程组
记载
《九章算术》方程章中
分类
数学
外文名
linear system of equations
包括
系数

初等变换

初等变换(elementary transformation)是三种基本的变换,出现在《高等代数》中。初等变换包括:线性方程组的初等变换、行列式的初等变换和矩阵的初等变换,这三者在本质上是一样的。

中文名
初等变换
归属学科
高等代数
包括
三种基本的变换
外文名
Elementary transformation
适用于
线性方程组;矩阵;行列式
应用
十分广泛

增广矩阵

增广矩阵(又称扩增矩阵)就是在系数矩阵的右边添上一列,这一列是线性方程组的等号右边的值。

中文名
增广矩阵
别名
扩增矩阵
领域
线性代数
外文名
Augmented matrix
解释
系数矩阵

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数学

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