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#1 2007-05-02 04:26:48

lulu1010
Guest

matrix cofactor?

hi. i dont get how you would find the matrix cofactor. could someone exlpain it to me please with this example. i know how to find the determinant, but not the cofactor. thanks for ur help!

example:

Matrix A:
[ 2 3 4 ]
[ 1 4 5 ]
[-2 1 0 ]         

det(A) = -4

matrix of cofactor is???

#2 2007-05-02 05:36:03

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: matrix cofactor?

First you need to find the matrix of minors.

To find the value of each element in that, you ignore the row and column that the corresponding element of A is in, then find the determinant of the resulting 2x2 matrix.

For example, the first element in the matrix of minors would be |4 5|, which is -5.
                                                                                            |1 0|

To get the matrix of cofactors, you just take the matrix of minors and multiply every other element in it by -1. The elements that you change should form a checkerboard pattern, with the top-left element being left alone.

Just so you can check, your answer should be:

(-5 -10 9)
( 4   8 -8)
(-1  -6  5)


Why did the vector cross the road?
It wanted to be normal.

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#3 2007-05-02 05:47:31

lulu1010
Guest

Re: matrix cofactor?

wow thanks alot! that certainly made things more clear now. thank you! smile)

#4 2007-05-03 04:21:28

lulu1010
Guest

Re: matrix cofactor?

hey. you know for the second one to work out '-10' i keep getting +10??

[ 1 5 ]
[-2 0 ]

(1 * 0) - (5 * -2) = +10

why is it +10??
thanks

#5 2007-05-03 04:24:42

lulu1010
Guest

Re: matrix cofactor?

oh i see the 'checkboard pattern'! sorry.. i get it now! smile

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