## Dido525 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) ?

1. Dido525

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

true because all would be 0

3. Outkast3r09

|dw:1359528317295:dw|

4. Dido525

That's such a stupid question then...

5. Dido525

Are you sure though? What if some of them are 17 and some of them are 1?

6. Dido525

0* now 1 sorry.

7. Dido525

not*

8. Dido525

Like if I change 2 of those to 0 the determininant become 4913 all of a sudden.

9. Outkast3r09

maybe thinking off this as M or C matrices i forgot what they're called

10. Dido525

Cofactor?

11. Outkast3r09

|dw:1359528522846:dw|

12. Outkast3r09

now each one of those cofactors i think they're called =|dw:1359528606154:dw|

13. Outkast3r09

that's why you'll get zero if you put 17's all in it

14. Dido525

Okay but what if I put SOME of them as 17 and SOME of them as 0. Then it a lot bigger.

15. Outkast3r09

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

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

|dw:1359528822331:dw|

18. Dido525

THat's 4913.

19. Dido525

SO clearly, there is a maximum.

20. Outkast3r09

|dw:1359528911003:dw|

21. Dido525

Nvm, I got it.

22. Outkast3r09

|dw:1359528962928:dw|

23. Outkast3r09

is this what you got?

24. Outkast3r09

so i'm thinking the rule is the largest determinant comes from having vectors that are dependent of one anothre

25. Outkast3r09

i mean independent

26. Outkast3r09

so the largest happens when all are independent of one another