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
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
|These are the ones that go along with our column.