有关解线性方程组的一些思考

Some Thoughts for Solving System of Linear Equations

解线性方程组是线性代数课程的最重要内容之一,目前工科线性代数的大纲和教材一般不包括不相容方程组,其实这部分内容具有广泛的应用.本文用微积分方法给出不相容方程组的最小二乘解以及极小范数最小二乘解,可供线性代数课程的教学改革作参考.建议待条件成熟时,将不相容方程组的最小二乘解纳入工科线性代数的教学大纲和教材.

Solving system of linear equations is one of the most important contents in linear algebra.The inconsistent equations are not contained in domestic teaching outline and textbooks of engineering linear algebra generally.Actually the inconsistent equations possess extensive application and are dealt with in many teaching textbooks abroad.Using calculus,this paper represents least-squire solution and minimum norm one for the inconsistent equations.It is suggested that least-squire solution should be brought into teaching outline and textbooks of engineering linear algebra.