5. Determinants

5.1.               Introduction

5.2.               Motivation for the Choice of Axioms for a Determinant Functions

5.3.               A Set of Axioms for a Determinant Function

5.4.               The Determinant of a Diagonal Matrix

5.5.               The Determinant of an Upper Triangular Matrix

5.6.               Computation of any Determinant by the Gauss-Jordan Process

5.7.               Uniqueness of the Determinant Function

5.8.               Exercises

5.9.               Multilinearity of Determinants

5.10.            Applications of Multilinearity

5.11.            The Product Formula for Determinants

5.12.            The Determinant of the Inverse of a Nonsingular Matrix

5.13.            Determinants and Independence of Vectors

5.14.            The Determinant of a Block-Diagonal Matrix

5.15.            Exercises

5.16.            Expansion Formulas by Cofactors

5.17.            The Cofactor Matrix

5.18.            Cramer’s Rule

5.19.            Expansion Formulas by Minors

5.20.            Exercises

5.21.            Existence of the Determinant Function

5.22.            Miscellaneous Exercises on Determinants

5.23.            Summary