Introduction to Engineering and Scientific Computing with Python

8 Solving Sets of Algebraic Equations

DOI: 10.1201/9781003256861-8

Chapter Objectives

• Review the scenario for sets of n linear equations in n unknowns.
• Know how to solve a 2 × 2 system of linear algebraic equations graphically and understand how this provides insight into singular and ill-conditioned systems.
• Understand the determinant of a square matrix and how it can be used to detect singular and ill-conditioned systems.
• Know how Cramer’s Rule uses determinants to solve a set of linear equations.
• Learn how to implement the Gaussian elimination method, and, from a vector/matrix perspective, how it achieves the solution of a set of linear algebraic equations.
• Understand the limitations of Gaussian elimination and how they can be overcome ...