现行六年制重点中学高中数学课本《代数》第二册第四章在讲三元线性方程组的解法时,对于系数行列式D=0时解的情况只说了一句话:“方程组或者无解或者有无穷多解(证明从略)”。(见上述课本P.146倒数第五行)。我在讲授这部分内容时,学生总是爱问:“什么情况下无解?什么情况下有无穷多解?这无穷多解如何表达出来?”为满足学生的求知欲望,同时培养学生分析问题和解决问题的能力,我使用下面的方法来解决问题,花的时间不多,而效果较好。现介绍如下,供读者参考。我们对照上述课本P.143的4.5节来阐述问题。为节省篇幅,许多符号都借用上述课本中已有的,此处不再赘述。比如,系数行列式用D表示,C_3表示D中元素c_3的代数余子式,等等。当D=0时,三元线性方程组解的情况可分 In the fourth chapter of the current six-year high school mathematics textbook “Algebra” in the second volume of the book, when we talk about the solution of the ternary system of linear equations, we only say one word for the case of the solution of the determinant D = 0: “The equations or No solution or infinite solution (proof is omitted).” (See the fifth last line of the above textbook P.146). When I was teaching this part of the content, students always loved to ask: “Under what circumstances there is no solution? Under what circumstances there are infinitely many solutions? How does this infinite solution be expressed?” to satisfy the students’ desire for knowledge while cultivating students to analyze problems and To solve the problem, I use the following method to solve the problem. It takes less time and works better. The following is introduced for readers’ reference. We address the issue against section 4.5 of the above textbook P.143. In order to save space, many symbols are borrowed from the textbooks mentioned above and will not be repeated here. For example, the determinant of the coefficient is denoted by D, C_3 represents the algebraic cofactor of the element c_3 in D, and so on. When D=0, the solution of the ternary system of linear equations can be divided