Balancing Chemical Reactions with Matrix Methods and Computer Assistance (UMAP)

A unit using matrix methods and computer assistance in balancing chemical reactions. The purpose of this module is to: 1) reinforce the abstract concept of linear independence by appealing to a concrete setting where the dimension exceeds 3; and 2) apply the inverse matrix method for solving linear systems to situations arising from chemical reactions.

Table of Contents:

1. INTRODUCTION

2. BACKGROUND: MATHEMATICAL AND CHEMICAL
2.1 Vectors in Two and Three Dimensions
2.2 A Word About Chemical Elements

3. SOLVING LINEAR SYSTEMS: THE INVERSE MATRIX METHOD

4. BALANCING CHEMICAL REACTIONS
4.1 The Computer Supplies a Readily Recognizable Answer
4.2 The Computer Supplies an Answer Which is Not Easily Recognized
4.3 Have We Only Dealt With Very Special Cases?
4.4 The Non-Unique Case

5. SUMMARY

6. EXERCISES

7. REFERENCES

8. ANSWERS TO EXERCISES