ENG EK 102 Lecture 5: Lecture 5&6(1)

• School: Boston University
• Department: Engineering Core
• Course: ENG EK 102
• Professor: John T Draper

Document Summary

Introduction to linear algebra for engineers (ek102 b1) Lecture 5 & 6: e cient solution of systems of linear equations. In this lecture we look at a more e cient approach to solving a linear system of equations many times when the matrix a does not change but the problem is posed with di erent. The key point of the idea is to avoid repeating the process of transform- ing a into its reduced row echelon form. We describe a method of remembering the process through encoding it in a matrix. Along the way, we introduce the notion of elementary matrices. Motivated by the example provided, we introduce the important notion of invertible (also called non-singular) square matrices. You will learn a systematic procedure for nding the inverse of a square matrix a, if it exists, or recognizing that the inverse does not exist, if that is the case.