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November 13th, 2011, 05:25 AM   #1
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determinant of BA.....

[color=#000000]Let and such that



what is the value of ?[/color]
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November 16th, 2011, 11:54 AM   #2
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Re: determinant of BA.....

Assuming there is enough information to solve this, then the precise A and B are not important. So just find A and B that work:
in particular

Calculate BA with those A and B and find its determinant.
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November 16th, 2011, 12:21 PM   #3
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Re: determinant of BA.....

2???
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November 17th, 2011, 01:49 AM   #4
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Re: determinant of BA.....

[color=#000000]Yes wnvl! The eigenvalues of the matrix AB are 0,1,2, so the characteristic polynomial of AB is



so the characteristic polynomial of BA is



meaning that det(BA)=2.[/color]
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November 17th, 2011, 01:59 AM   #5
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Re: determinant of BA.....

Quote:
Originally Posted by ZardoZ
[color=#000000]Yes wnvl! The eigenvalues of the matrix AB are 0,1,2, so the characteristic polynomial of AB is



so the characteristic polynomial of BA is



meaning that det(BA)=2.[/color]
Just said 2 after reading the post of HallsofIvy.



Didn't know that theorema, but not unlogic.
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November 17th, 2011, 02:20 AM   #6
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Re: determinant of BA.....

[color=#000000]Yes but HallsofIvy made an assumption that might have led to "questionable" conclusions.[/color]
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