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A linear Algebra Problem (3x3 Matrix)

  1. Jan 31, 2013 #1
    1. The problem statement, all variables and given/known data
    I want to proove the determinant of the following 3x3 matrix is 0.

    1 1 1

    tanA tanB tanC

    tan2A tan2B tan2C

    where A+B+C=2pi.


    2. Relevant equations

    Sorry I don't know how to type here so I show in the attachment.

    3. The attempt at a solution

    Sorry I have attempted but found no way closed to the solution.
     

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    Last edited: Jan 31, 2013
  2. jcsd
  3. Jan 31, 2013 #2

    HallsofIvy

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    If you want to do it then you first have to attempt to do it and you have shown no attempt. Under "relevant equations" you might put something like
    [tex]\left|\begin{array}{ccc}a & b & c \\ d & e & f \\ g & h & i\end{array}\right|= a\left|\begin{array}{cc}e & f \\ h & i\end{array}\right|- b\left|\begin{array}{cc}d & f \\ g & i\end{array}\right|+ c\left|\begin{array}{cc}d & e \\ g & h\end{array}\right|[/tex]
    as well as some trig identities like
    [tex]tan(2A)= \frac{2tan(A)}{1+ tan^2(A)}[/tex]
     
    Last edited: Jan 31, 2013
  4. Jan 31, 2013 #3
    f
    Sorry it is my bad. Thanks!
     
    Last edited by a moderator: Jan 31, 2013
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