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

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Dido525Best ResponseYou've already chosen the best response.0
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.
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
true because all would be 0
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
dw:1359528317295:dw
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
That's such a stupid question then...
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Are you sure though? What if some of them are 17 and some of them are 1?
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Like if I change 2 of those to 0 the determininant become 4913 all of a sudden.
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
maybe thinking off this as M or C matrices i forgot what they're called
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
dw:1359528522846:dw
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
now each one of those cofactors i think they're called =dw:1359528606154:dw
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
that's why you'll get zero if you put 17's all in it
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
Okay but what if I put SOME of them as 17 and SOME of them as 0. Then it a lot bigger.
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
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
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
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
 one year ago

Dido525Best ResponseYou've already chosen the best response.0
SO clearly, there is a maximum.
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
dw:1359528911003:dw
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
dw:1359528962928:dw
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
is this what you got?
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
so i'm thinking the rule is the largest determinant comes from having vectors that are dependent of one anothre
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
i mean independent
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
so the largest happens when all are independent of one another
 one year ago
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