从线性方程组“看”课堂教学在科研及工程实践中的应用

Application of the “look” teaching of the linear equations in the research and engineering practice

线性方程组不仅是"线性代数"的重要内容,也是科学研究和工程应用的基础知识。线性方程组分为适定、欠定和超定3种,但在"线性代数"课堂教学中往往仅涉及适定和欠定两种情况,而且欠定时仅给出由基础解系表示的解空间。文章从线性方程组的课堂教学入手,探讨了线性代数知识在科学研究和工程应用中的拓展。以"线性代数"课程中的线性方程组为例,探讨分析了在课堂教学中将基础知识延伸至科研热点和工程应用中的可行性。

The system of linear equations is not only the important content of the "Linear Algebra", but also the basic knowledge of scientific research and engineering application. The system of linear equations is divided into three types, which are suitable, underfixed and overfixed. However, in the "Linear Algebra" class teaching, only two cases of proper and undefinite are involved, and the undertiming only gives out the solution space indicated by the basic solution. This paper starts with the classroom teaching of linear equations, and discusses the development of linear algebra knowledge in scientific research and engineering application. Taking the system of linear equations in the "Linear Algebra" course as an example, the feasibility of extending the basic knowledge to the hot spot of scientific research and the application of engineering is discussed.