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Determinate question

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data
    [URL]http://74.52.147.194/~devilthe/uploads/1318251620.png[/URL]


    2. Relevant equations
    None


    3. The attempt at a solution
    I asked my teacher the same question and she said this:

    Okay, so I know that when you multiple a row of a matrix by a scalar, the determinate also gets multiplied by that same scalar.

    Know from the question that it's a 2x2 matrix we're dealing with.

    Know that the determinate of a 2x2 matrix is ad-bc

    I have no idea how to do this question it's the only one I can't get out of the whole assignment...


    I still can't get it lol

    Any help would be appreciated!

    Thanks,
    Elliott
     
    Last edited by a moderator: Apr 26, 2017
  2. jcsd
  3. Oct 9, 2011 #2

    NascentOxygen

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    Write down the 2x2 matrix whose determinate is ad - bc
    Let's call this matrix A.
    Write down matrix -3A
    Determine the determinate of this matrix.
    Compare with above.
     
  4. Oct 9, 2011 #3

    SammyS

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    So, for -3 A, how many rows get multiplied by -3 ?
     
  5. Oct 9, 2011 #4
    Alright so I got it at 27. I did the matrix out like NascentOxygen said and it made more sense.

    To answer your question SammyS, both rows get multiplied by -3 (now I see that).

    I still don't see how this question is relevant to this problem, though:

     
  6. Oct 9, 2011 #5

    SammyS

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    For each row of the matrix that you multiply by -3, multiply the corresponding determinant by -3.
     
  7. Oct 10, 2011 #6

    NascentOxygen

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    27? I wasn't expecting that for the answer.
     
  8. Oct 10, 2011 #7
    Yup. What were you expecting then? :S
     
  9. Oct 10, 2011 #8

    HallsofIvy

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    Both rows got multiplied by -3 so the entire determinant was multiplied by (-3)(-3)= 9. Since the original determinant was 3, the new determnant will be (3)(9)= 27 as you say you got.
     
  10. Oct 10, 2011 #9

    NascentOxygen

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    I had in mind completing the answer as: det(-3A) = 9.det(A)
    since it seemed you already had the answer partly filled in.

    I'd overlooked being told det(A) =3.

    So 27 is good.
     
    Last edited: Oct 10, 2011
  11. Oct 10, 2011 #10

    HallsofIvy

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    ??? Where did he say what his teacher's answer was?
     
  12. Oct 10, 2011 #11

    NascentOxygen

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    I took it that teacher's answers are those in the boxes, and I looked at the one where he couldn't get the teachers answer. (Now seems unlikely!)

    I answered it as: 9*det(A)
    to accommodate that 9.
     
    Last edited: Oct 10, 2011
  13. Oct 10, 2011 #12

    SammyS

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    I think OP's answers are the ones in the boxes & the one boxed in red is wrong.
     
  14. Oct 11, 2011 #13
    Hahah sorry for the confusion but yes this guy hit it spot on.

    Those are my answers in the box and I had already put an answer in to try it because it tells you whether you're right or wrong. I have unlimited tries.

    Probably should have posted it without an answer in the box but you get the idea...

    Thanks everyone!
     
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