anonymous
  • anonymous
Let A be a 3 × 3 matrix whose entries are 17 or 0. What is the largest possible value for det(A) ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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.
anonymous
  • anonymous
true because all would be 0
anonymous
  • anonymous
|dw:1359528317295:dw|

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

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