angela210793
  • angela210793
How to prove that det|A|=det|AT| AT=transposed matrix
Mathematics
katieb
  • katieb
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katieb
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anonymous
  • anonymous
Take any general 3X3 matrix and find its determinant... Again take the transpose of the same matrix and find its determinant.. Both will come same...
amistre64
  • amistre64
proof by example?
anonymous
  • anonymous
Taking general example like taking variable like a b c etc..

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angela210793
  • angela210793
or maybe prove tht det|A| doesn't change wqhen u change the places of two rows or columns @amistre64 not example...i need it in general with |dw:1341513981391:dw|
amistre64
  • amistre64
right, prove it with an nxn ....
amistre64
  • amistre64
det goes negative when you swap rows or cols i think
angela210793
  • angela210793
i dont even remember wht happens...and i read it 3 hrs ago -_-
amistre64
  • amistre64
id hate to try to do an induction proof with it tho
amistre64
  • amistre64
wouldnt the transpose be the same as running the determinant down the rows instead of across the columns?
amistre64
  • amistre64
|dw:1341514233970:dw|
amistre64
  • amistre64
|dw:1341514301567:dw|
amistre64
  • amistre64
dunno how much of a proof that is tho :)
angela210793
  • angela210793
haha..its ok...:D thanks anyway :)
amistre64
  • amistre64
... good luck ;)
angela210793
  • angela210793
Thanks...i really need it :(
anonymous
  • anonymous
Its a pretty hard proof, I had to do it in my intro proofs class. Here's this: https://www.projectrhea.org/rhea/index.php/Determinant_Transpose_Proof Will help some I think :P
angela210793
  • angela210793
@malevolence19 THANK YOU!!!!!!!!! :D

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