行列式计算的若干方法

Some Methods of Calculating the Determinant

行列式是高等代数课程中的一个基本概念,是探讨线性方程组的重要工具之一。行列式计算方法灵活多样,其计算要依据行列式的特点选取恰当的方法。本文通过对行列式的定义及性质的研究,探讨了具体型行列式及抽象型行列式的若干计算方法,如加边法、拆项法、析因子法,并通过具体例题分析这些方法的应用,为后续的学习提供更加全面的指引与参考。

Determinant is a basic concept in advanced algebra course and one of the important tools to explore linear equations. The determinant calculation method is flexible and diverse, and the calculation should choose the appropriate method according to the characteristics of the determinant. Through the study of the definition and nature of determinant, this paper discusses some calculation methods of concrete determinant and abstract determinant, such as edge addition method, dissolving method, factor analysis method, and analyzes the application of these methods through specific examples, so as to provide more comprehensive guidance and reference for the follow-up study.