Dido525
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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Dido525
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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.
Outkast3r09
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true because all would be 0
Outkast3r09
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|dw:1359528317295:dw|
Dido525
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That's such a stupid question then...
Dido525
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Are you sure though? What if some of them are 17 and some of them are 1?
Dido525
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0* now 1 sorry.
Dido525
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not*
Dido525
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Like if I change 2 of those to 0 the determininant become 4913 all of a sudden.
Outkast3r09
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maybe thinking off this as M or C matrices i forgot what they're called
Dido525
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Cofactor?
Outkast3r09
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|dw:1359528522846:dw|
Outkast3r09
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now each one of those cofactors i think they're called =|dw:1359528606154:dw|
Outkast3r09
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that's why you'll get zero if you put 17's all in it
Dido525
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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.
Outkast3r09
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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
Outkast3r09
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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
Dido525
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|dw:1359528822331:dw|
Dido525
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THat's 4913.
Dido525
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SO clearly, there is a maximum.
Outkast3r09
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|dw:1359528911003:dw|
Dido525
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Nvm, I got it.
Outkast3r09
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|dw:1359528962928:dw|
Outkast3r09
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is this what you got?
Outkast3r09
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so i'm thinking the rule is the largest determinant comes from having vectors that are dependent of one anothre
Outkast3r09
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i mean independent
Outkast3r09
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so the largest happens when all are independent of one another