浅谈行列式和矩阵的计算方法及应用

摘要：行列式和矩阵是线性代数最基本内容之一,是研究线性代数的重要工具。本文根据行列式和矩阵的特点，通过例题的形式，列举行列式和矩阵的几种计算方法；化为已经熟悉的行列式计算降阶法、拆项法、加边法，并指明了这些方法使用条件但这几种方法之间不是相互独立，而是相互联系的，有时几种方法结合着用效果更好。本文还介绍了矩阵的运算方法（如数乘）。又介绍了行列式和矩阵的简单应用，其中包括应用行列式计算矩阵的逆矩阵。应用矩阵解线性方程组，无论是在介绍行列式和矩阵的计算方法还是在介绍行列式和矩阵的应用中，本文都提供了相应的例题，便于对照学习，以达到最佳的学习效果。使我们对行列式和矩阵有了更深更广泛的理解。
关键词：行列式； 矩阵； 计算方法； 应用
A shallow Discussion on the methods and the application of the Determinant and Matrix computation
Abstract: The determinant which is one of  the most basic elements of the linear algebra, and the matrix have been used widely and importantly. according to their own characters, this paper lists some calculation methods on the determinant and the matrix computation by way of some amples such as familiar reduction methods and adding with their using conditions. However, these methods have a lose relationship with each other, and we can get better resulfs if combing them together. In addition, this paper introduces the application methods of the matrix. And the determinant, including theapplication determinant to solue the question of linear epuations. and the inver matrix. The auther comes up with some examples not only in the determinant calculation methods but also in its applications in order to get the best effort. Therefore, we can have a wider and deeper understanding of the determinant and matrix. 
Key words: Application determinant matrix calculation method

目      录

1 计算行列式的若干基本方法……………………………………………………………2
1…1 化为已经熟悉的行列式来计算………………………………………………2
1…2 降阶法………………………………………………………………………………5
1…3 拆项法…………………………………………………………………………5
1…4 加边法………………………………………………………………………………6
2 矩阵的运算………………………………………………………………………………8
2…1 乘法…………………………………………………………………………………………8
2…2 矩阵的转置……………………………………………………………………………10
3 行列式和矩阵的应用………………………………………………………………………………12
3…1 行列式在求逆矩阵中的应用…………………………………………………………………12
3…2 矩阵在解线性方程组方面的应用……………………………………………………………13
参考文献………………………………………………………………………………………16
致谢……………………………………………………………………………………………17