SOLUTION: i got this matrix : 3 0 0 -1 0 2 -2 1 -3 3 -2 2 6 1 0 1 i want to find the determinant, i got this : |2 -2 1| | 0 2 -2| 3 |3 -2 2|- 0 + 0 + |-3 3 -2|

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Question 831410: i got this matrix :
3 0 0 -1
0 2 -2 1
-3 3 -2 2
6 1 0 1
i want to find the determinant, i got this :
|2 -2 1| | 0 2 -2|
3 |3 -2 2|- 0 + 0 + |-3 3 -2|
|1 0 1| | 6 1 0|
and got 3((2x-2)+(2x1)+2)+(42+42) = 84 ?
where do i got wrong ?
Found 2 solutions by Elomeht, AnlytcPhil:
Answer by Elomeht(22)   (Show Source): You can put this solution on YOUR website!
The correct answer is 18.
It is very cumbersome to write in this forum.
Send me a "thank you" note and I will get it out to you in a PDF format.
Sorry, but it takes me forever to do it by long hand in this forum.
Best regards.
Answer by AnlytcPhil(1807)   (Show Source): You can put this solution on YOUR website!
Don't listen to him.  You can't stop and go "PDF-ing" everytime you need 
to do a small problem.  

First get a 0 in the upper left corner by multiplying the 4th column by 3
and adding it to the first column.  
     
| 3  0  0 -1|               | 0  0  0 -1|         | 3  2 -2|    | 3  2 -2|
| 0  2 -2  1|  3C4+C1->C1   | 3  2 -2  1|  = -(-1)| 3  3 -2| =  | 3  3 -2|
|-3  3 -2  2|               | 3  3 -2  2|         | 9  1  0|    | 9  1  0|
| 6  1  0  1|               | 9  1  0  1|

When you get down to a 3×3 determinant, it's often too tedious to
always expand it by minors.  I'm sure your error was a sign or 
something.  Expand by minors until you get down to a 3×3, then
do the 3×3 this following way.  You're less likely to make a mistake.
Copy the first two columns over to the right of the determinant

| 3  2 -2| 3  2
| 3  3 -2| 3  3
| 9  1  0| 9  1

Then multiply the three diagonals that slant this way \ and add them:

(3)(3)(0) + (2)(-2)(9) + (-2)(3)(1) = 0-36-6 = -42

Then multiply the three diagonals that slant this way / and add them

(-2)(3)(9) + (3)(-2)(1) + (-2)(3)(0) = -54 - 6 - 0 = -60

Then subtract (-42)-(-60) = -42 + 60 = 18

Edwin
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