关于两个线性方程组同解问题教学的思考

On the Teaching of Two Systems of Linear Equations with Same Solutions

探讨教学中如何引导学生理解和掌握线性方程组同解的问题。首先通过对消元法理解,得出两个线性方程组同解的充分条件;其次利用矩阵的初等变换和初等矩阵的知识,得出两个线性方程组同解的必要条件;再者,通过理解系数矩阵列向量组与同解的关系,给出求一个向量组的极大无关组的方法。最后是怎样从内积的角度去看待同解问题。

It is discussed that how to teach students to understand and master the problems about same solutionsof two systems of linear equations. Firstly, the sufficient condition of same solutions problem is introduced bycomprehending the elimination. Secondly, the necessary condition of it is given by understanding elementarytransformations and elementary matrices. Then, we give a way to find out maximal independent systems from theconcept of the same solutions. Lastly, we explore how to deal with the same solution problems by scalar productin Euclidean spaces.