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Linear Algebra: Determinant 
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#1
Feb2112, 10:18 AM

P: 9

I need help with another homework problem
Let n be a positive integer and A_{n*n} a matrix such that det(A+B)=det(B) for all B_{n*n}. Show that A=0 Hint: prove property continues to hold if A is modified by any finite number of row or column elementary operations It seems obvious that A=0 but i'm having trouble developing the proof. Any help would be great. 


#2
Feb2112, 10:36 AM

Mentor
P: 18,327

Please post homework in the homework forum. I moved it for you now.
A hint for the proof: can you write a row/column operation as an elementary matrix?? 


#3
Feb2112, 11:03 AM

P: 9

Yes and the product of the elementary matrices returns
A=E_{1}*E_{2}*..*E_{n} is this what you are referring to? 


#4
Feb2112, 11:05 AM

Mentor
P: 18,327

Linear Algebra: Determinant
Yes. Let E be an elementary matrix, can you show that
[tex]det(EA+B)=det(B)[/tex] ?? 


#5
Feb2112, 11:49 AM

P: 9

Im not quite sure how to show this



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