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几类与矩阵的秩有关的问题

Several types of issues related to the rank of

matrix

专 业: 数学与应用数学

作 者:

指导老师:

学校 二○一

摘 要

本文研究了与矩阵的秩有关的几类问题, 用定理和实例说明了矩阵的秩在向量的线性关系; 求解线性方程组; 判断空间中点线面的位置关系; 二次型; 线性变换等方面的应用.

关键词: 矩阵的秩; 向量; 线性方程组; 位置关系; 二次型; 线性变换

Abstract

This article study several types of issues related to the rank of matrix, theorem and the examples used the rank of the matrix in the linear relationship between vector, solving linear equations, determine spatial point

line

surface

location

relationship,

quadratic,

linear

transformationand other applications.

Keywords: Rank of matrix; Vector; Linear equations; Set relations;

Quadratic; Linear transformationand