Matrix Determinants

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Hey y'all well I'm having major problems trying to figure out matrix determinants. I keep trying and trying but getting a totally diffrent answer from what the back of the book says...

[12, 4, -6]
[ 2, 1, 3 ]
[1, 0, -2 ]

I dont know if the way I typed that is understandable but that's the determinant which is a 3 x 3 and I'm supposed to evaluate it and everytime I try and evalute it, I always end up with -34 and the back of my book says the answer is 10 and I am so way totally stuck so if someone could help me, it would be greatly appreciated.

Thanks ~*
 
To make characters stay where you put them, try using the "code" tags:

Code: 
  | 12   4  -6 |
  |  2   1   3 |
  |  1   0  -2 |
I'm getting the book's answer. Please reply with your steps, so we can try to figure out where the error is coming in. Thank you.

Eliz.
 
I multipled:

12 x 1 x -2 = -24
4 x 3 x 1 = 12
-6 x 2 x 0 = 0

Which is the first part of the problem
Then I did:

1 x 1 x -6 = -6
0 x 3 x 12 = 0
-2 x 2 x 4 = -16

Then set up my equation :

(-24 -12 -0) - (-6-0+16)
= -36-10 = -46

Okay, so I'm getting a different answer everytime. I even tried solving the equation two different ways, that was the first, the second is:

24+12+0+6-0+16=10

Whoa! Okay so maybe I got the answer solving it that way, but my teacher had shown me the first way and it was messing me up over and over, so I dont really know what I was doing wrong, but thanks.
[/code]
 
You switched a sign. When you multiplied, you got -24, 12, 0, and then -6, 0, 16. But when you added, you switched the "12" to a "-12".

You appear to be conflating two methods: "by cofactors" and the multiplication method. When you do the multiplication in the way you are, you have to add all the "down and to the right" values, and then subtract all the "up and to the right" values. You only alternate the signs in the "by cofactors" method.

Eliz.
 
Haha, I feel dumb, I spent about 45 mintues trying to figure out what I did wrong and it was a carless sign error. Thanks so much!
 
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