Problem Solving with Linear Systems of Equations Using Linear Algebra Techniques

This chapter aims to set up a system of equations to solve a problem, and recognize unique solutions, no solution and infinite solutions as results. It illustrates the use of systems of equations to solve real-world applications from the sciences, engineering, and economics. There are exactly three possibilities for a system of linear equations: the system has a unique solution, an infinite number of solutions, or no solution. The Linear Algebra module has been designed to accommodate different sets of usage scenarios: casual use and programming use. Load the linear algebra package, enter the system’s matrix in augmented form, row reduce the matrix using Gaussian elimination, and then interpret the results. Balancing chemical equations can be an application of solving a system of linear equations. Placing variables as the multipliers for each compound and making equations for each type of atom in the reaction results in a system of linear equations.