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 2 years ago
Let A be a 3 × 3 matrix whose entries are 17 or 0. What is the largest possible value for det(A) ?
 2 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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Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0Since 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
 2 years ago
Best ResponseYou've already chosen the best response.0true because all would be 0

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1359528317295:dw

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0That's such a stupid question then...

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0Are you sure though? What if some of them are 17 and some of them are 1?

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0Like if I change 2 of those to 0 the determininant become 4913 all of a sudden.

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0maybe thinking off this as M or C matrices i forgot what they're called

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1359528522846:dw

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0now each one of those cofactors i think they're called =dw:1359528606154:dw

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0that's why you'll get zero if you put 17's all in it

Dido525
 2 years ago
Best ResponseYou've already chosen the best response.0Okay but what if I put SOME of them as 17 and SOME of them as 0. Then it a lot bigger.

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0there 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
 2 years ago
Best ResponseYou've already chosen the best response.0because 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
 2 years ago
Best ResponseYou've already chosen the best response.0SO clearly, there is a maximum.

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1359528911003:dw

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1359528962928:dw

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0is this what you got?

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0so i'm thinking the rule is the largest determinant comes from having vectors that are dependent of one anothre

Outkast3r09
 2 years ago
Best ResponseYou've already chosen the best response.0so the largest happens when all are independent of one another
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