ABSTRACT
In this chapter, the authors develop the theory of determinants based on three axioms. Some of the computations are tedious, but they are presented for several reasons, including the derivation of the formula for the determinant given in more advanced settings. Determinants have a variety of uses in linear algebra, including solving systems of linear equations, determining whether a square matrix is invertible, and determining whether a collection of vectors form a basis. Computing a determinant can be quite tedious without a computer and understanding how the computation formulas arose can be nonintuitive. Approach to determinants relies on the geometric idea of measuring the change in the volume of a parallelepiped under a linear transformation.
