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angela210793

How to prove that det|A|=det|AT| AT=transposed matrix

  • one year ago
  • one year ago

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  1. waterineyes
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    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...

    • one year ago
  2. amistre64
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    proof by example?

    • one year ago
  3. waterineyes
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    Taking general example like taking variable like a b c etc..

    • one year ago
  4. angela210793
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    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|

    • one year ago
  5. amistre64
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    right, prove it with an nxn ....

    • one year ago
  6. amistre64
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    det goes negative when you swap rows or cols i think

    • one year ago
  7. angela210793
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    i dont even remember wht happens...and i read it 3 hrs ago -_-

    • one year ago
  8. amistre64
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    id hate to try to do an induction proof with it tho

    • one year ago
  9. amistre64
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    wouldnt the transpose be the same as running the determinant down the rows instead of across the columns?

    • one year ago
  10. amistre64
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    |dw:1341514233970:dw|

    • one year ago
  11. amistre64
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    |dw:1341514301567:dw|

    • one year ago
  12. amistre64
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    dunno how much of a proof that is tho :)

    • one year ago
  13. angela210793
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    haha..its ok...:D thanks anyway :)

    • one year ago
  14. amistre64
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    ... good luck ;)

    • one year ago
  15. angela210793
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    Thanks...i really need it :(

    • one year ago
  16. malevolence19
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    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

    • one year ago
  17. angela210793
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    @malevolence19 THANK YOU!!!!!!!!! :D

    • one year ago
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