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By this point in your mathematical career you should have
run across functions. The functions that
you’ve probably seen to this point have had the form 
where x
is a real number and the output of the function is also a real number. Some examples of functions are and .
Not all functions however need to take a real number as an
argument. For instance we could have a
function that takes a matrix X and outputs a real number.
In this chapter we are going to be looking at one such function, the
determinant function. The determinant
function is a function that will associate a real number with a square
matrix.
The determinant function is a function that won’t be seeing
all that often in the rest of this course, but it will show up on occasion.
Here is a listing of the topics in this chapter.
The Determinant Function We will give the formal definition of the
determinant in this section. We’ll also
give formulas for computing determinants of and matrices.
Properties of Determinants Here we will take a look at quite a few
properties of the determinant function.
Included are formulas for determinants of triangular matrices.
The Method of Cofactors In this section we’ll take a look at the first
of two methods form computing determinants of general matrices.
Using Row Reduction to Find Determinants Here we will take a look at the second method
for computing determinants in general.
Cramer’s Rule We will take a look at yet another method for
solving systems. This method will
involve the use of determinants.