If A and B are matrices n*n and their rank is n each. How do you proove that: Det(A+B)<=2*Det(A*B)? Please help!!!! Thanks in advance

*cough* homework *cough*

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Indeed. This isn''t a forum for solving homework problems Mr. God.

Lets hope it gets closed before anyone actually answers this...

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quote:

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Original post by The C modest god
How do you proove that:
Det(A+B)<=2*Det(A*B)?

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I usually use pen and paper. I would use pencils, but I don''t have a pencil sharpener.

uhm, is this a joke? the statement lacks truth.

just consider the case when a=b=0.5I where I is an nxn identity matrix.

det(a+b) = det(0.5I + 0.5I) = det(I) = 1
2*det(a*b) = 2*det(a)*det(b) = 2*(0.5^2)*(0.5^2) = 2*0.5^4 = 1/8

clearly 1 is not less than or equal to 0.125

quote:

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Original post by The C modest god
How do you proove that:
Det(A+B)<=2*Det(A*B)?

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I go to an internet forum and ask them to do it for me.

FrigidHelix : det() is n-linear so

det( 0.5 I ) = 0.5^n

However, your statement still holds, except for n=0.

ToohrVyk

ya, my bad. i wrote the example for 2x2

Yeah, this is homework. And I''m closing the thread.

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I like Jambolo''s reply, though.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.