Determinants for 3 x 3's are a little messier than they are for 2 x 2's.  The determinants for 2 x 2's were a snap to crunch, so what we'll do is break down our big 3 x 3 guys into easy 2 x 2 critters.

Let's just jump right in and do one:

Here's what you do:

Grab the row or column with the easiest numbers in it...  Column 1 looks easy.

What we're going to do is called "expanding about the first column."

Before we start, we need a grid of +'s and -'s...  Always start with a + in the upper left corner and go every other one:

I'll call this our "sign box."

 

These are the ones that go along with our column.