基于营养搭配餐问题探究线性方程组的解法

Exploring Solutions to Systems of Linear Equations Based on the Problem of Nutritious Meal Combinations

摘要: 线性方程组是线性代数中的一个重要分支，也是线性代数的基础，它贯穿了线性代数的大的部分内容，以线性代数为基础，可以解方程组，求解各类方程组解的问题，以及利用线性方程组解决矩阵的问题等。在实际生活中，线性方程组的应用也广泛，本文着重于从人体所需的营养物质问题出发，探究线性方程组的求解过程，最后得出结论，利用消元法，矩阵的初等变换来求解线性方程组。得到了关于非齐次线性方程组的解的判定方法以及求解过程。

Abstract: Linear equations are an important branch and foundation of linear algebra, permeating most of its content. Based on linear algebra, one can solve systems of equations and various problems related to solving systems of equations, and matrix problems have been solved using linear equations. In real life, linear equations are widely applied. This article focuses on the issue of nutrients required by the human body, exploring the process of solving linear equations. Finally, it concludes that linear equations can be solved using the method of elimination and elementary matrix transformations. The determination method and solving process for the solutions of non-homogeneous linear equations are obtained.