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#1 2007-06-21 17:35:54

lexmark
Member
Registered: 2007-06-21
Posts: 1

determinants

for the matrix A=4 -2 9
                        10 3 9
                        -6 7 1

a. find the minor of the element 3

b. find the coafactor of the element 7


answer is a. M22= 4  9
                           -6 1

b. is C32=- 4 9
                 10 9

I understand a. answer
I do not understand b. answer i do not understand how 10 and 9  is the answer.

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#2 2007-06-21 17:37:21

lexmark
Member
Registered: 2007-06-21
Posts: 1

Re: determinants

Cofactor

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#3 2007-06-21 17:37:45

lexmark
Member
Registered: 2007-06-21
Posts: 1

Re: determinants

please help me

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#4 2007-06-21 19:15:46

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

Re: determinants

[Moved to Help Me]

The answer is right. The cofactor of an element is exactly the same as its minor, except that it might be multiplied by -1 depending on which element it is.

For an element in the ith row and jth column of the original matrix, its cofactor would be its minor multiplied by (-1)^(i+j). In this case, i+j = 5 and so it would be multiplied by -1.


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

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#5 2007-06-22 05:56:06

lexmark
Member
Registered: 2007-06-21
Posts: 1

Re: determinants

could you please show me step by step b is correct

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#6 2007-06-22 07:04:42

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

Re: determinants

Well, you know how to find the minor of the matrix, because you did that for a.
Eliminating the 3rd row and 2nd column of matrix A gives you the minor:

4    9
10  9

Then you need to multiply by -1 to turn that into the cofactor, for the reason I gave in the post above.


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

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