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Question 549763: calculate the cofactor of the element 9 of this determinant
1 2 3 4
6 7 8 9
-1 -2 -3 -4
-6 -7 -8 -9
Help me please. Thank you
Answer by mathie123(224)   (Show Source):
You can put this solution on YOUR website! Okay so when doing cofactors, think of it as a checkerboard I find helps...
The top left is positive, and then every other changes sign. So that means when finding the cofactor of 9, it will be positive.
From there we take out the row and column that the 9 is in and find the determinant . This means we find the determinent of A(that's what I will call this next matrix)
1 2 3
-1 -2 -3
-6 -7 -8
So we just need to find this determinant.
Well going along the top row, we have
detA=1*detB-2*detC+2*detD
where B=
-2 -3
-7 -8
so detB=(-2*-8)-(-3*-7)=16-21=-5
And C=
-1 -3
-6 -8
So detC=(-1*-8)-(-3*-6)=8-18=-10
and D=
-1 -2
-6 -7
So detD=(-1*-7)-(-2*-6)=7-12=-5
Since detA=cofactor of 9=1*detB-2*detC+2*detD
We can plug in the values we have figured out and solve for this. I will leave this up to you :)
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