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Dido525

  • 3 years ago

Let A be a 3 × 3 matrix whose entries are 17 or 0. What is the largest possible value for det(A) ?

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  1. Dido525
    • 3 years ago
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    Since it say's OR I am actually not sure how I would do this. Setting all the entries to 17 simply makes the determinant 0.

  2. Outkast3r09
    • 3 years ago
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    true because all would be 0

  3. Outkast3r09
    • 3 years ago
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    |dw:1359528317295:dw|

  4. Dido525
    • 3 years ago
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    That's such a stupid question then...

  5. Dido525
    • 3 years ago
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    Are you sure though? What if some of them are 17 and some of them are 1?

  6. Dido525
    • 3 years ago
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    0* now 1 sorry.

  7. Dido525
    • 3 years ago
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    not*

  8. Dido525
    • 3 years ago
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    Like if I change 2 of those to 0 the determininant become 4913 all of a sudden.

  9. Outkast3r09
    • 3 years ago
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    maybe thinking off this as M or C matrices i forgot what they're called

  10. Dido525
    • 3 years ago
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    Cofactor?

  11. Outkast3r09
    • 3 years ago
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    |dw:1359528522846:dw|

  12. Outkast3r09
    • 3 years ago
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    now each one of those cofactors i think they're called =|dw:1359528606154:dw|

  13. Outkast3r09
    • 3 years ago
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    that's why you'll get zero if you put 17's all in it

  14. Dido525
    • 3 years ago
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    Okay but what if I put SOME of them as 17 and SOME of them as 0. Then it a lot bigger.

  15. Outkast3r09
    • 3 years ago
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    there was also a theory i think if i remember that if you somehow prove that two vectors are just combinations of the other... then you can prove it's zero also

  16. Outkast3r09
    • 3 years ago
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    because if two are the combinations of each other than you can reduce them down to [17 17 17] and then if you can easily get a row of zeroes

  17. Dido525
    • 3 years ago
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    |dw:1359528822331:dw|

  18. Dido525
    • 3 years ago
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    THat's 4913.

  19. Dido525
    • 3 years ago
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    SO clearly, there is a maximum.

  20. Outkast3r09
    • 3 years ago
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    |dw:1359528911003:dw|

  21. Dido525
    • 3 years ago
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    Nvm, I got it.

  22. Outkast3r09
    • 3 years ago
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    |dw:1359528962928:dw|

  23. Outkast3r09
    • 3 years ago
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    is this what you got?

  24. Outkast3r09
    • 3 years ago
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    so i'm thinking the rule is the largest determinant comes from having vectors that are dependent of one anothre

  25. Outkast3r09
    • 3 years ago
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    i mean independent

  26. Outkast3r09
    • 3 years ago
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    so the largest happens when all are independent of one another

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