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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:

| row 1: -2 , -9 , 4  row 2: 3 , 7 , -5  row 3: 1 , -6 , 8 |

Here's what you do:

Grab the row or column
with the easiest numbers
in it...  Column 1 looks
easy.
| row 1: -2 , -9 , 4  row 2: 3 , 7 , -5  row 3: 1 , -6 , 8 | ... put a box around column 1

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:

| row 1: + , - , +  row 2: - , + , -  row 3: + , - , + |

I'll call this our
"sign box."

 

These are the ones that go along with our column. | row 1: + , - , +  row 2: - , + , -  row 3: + , - , + | ... put a box around column 1