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高中数学第三册第一章有关三阶行列式的内容,定理多、题目变化大,是教学中的难点。总结解题方法,让学生掌握解题规律,特别是第三节定理4推论1和定理7的使用方法,是突破难点的关键。一、三阶行列式性质定理4推论1与性质定理7的综合运用。学会使用这两条性质是解决各类行列式习题的基础。而使用这两条性质的关键是全面分析行列式中行与行(或列与列)元素间的和、差、倍关系。把关系弄清后,就可利用这两条性质使行列式简化或变形成某种确定的形式。
The content of the third-order determinant in the first chapter of the third volume of high school mathematics, with many theorems and large changes in the subject, is a difficult point in teaching. Summarizing the problem-solving method to allow students to master the law of problem solving, especially the use of inferences 1 and 7 of Theorem 4 in the third section, is the key to breaking through the difficulties. The first and third-order determinant property theorem 4 The comprehensive application of Corollary 1 and Property Theorem 7 . Learning to use these two properties is the basis for solving all kinds of determinant exercises. The key to using these two properties is a comprehensive analysis of the sum, difference, and times of the elements of the determinant in the row and row (or column and column). After clarifying the relationship, these two properties can be used to simplify or change the determinant into a definite form.