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CHAPTER

Determinants

I N T R O D U C T I O N : We are all familiar with functions such as and , which associate a real number

with a real value of the variable . Since both and assume only real values, such functions are described as

real-valued functions of a real variable. In this section we shall study the “determinant function,” which is a real-valued

function of a matrix variable in the sense that it associates a real number with a square matrix . Our work on

determinant functions will have important applications to the theory of systems of linear equations and will also lead us to an
explicit formula for the inverse of an invertible matrix.

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