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Determinants of a matrix

  1. Oct 25, 2007 #1
    1. The problem statement, all variables and given/known data
    A 2 x 2 matrix B satisfies

    B (3 1)[tex]^{T}[/tex] = B (5 2)[tex]^{T}[/tex]

    What is det (B) ? Give a reason


    2. Relevant equations

    None really

    3. The attempt at a solution

    I really have no idea how to start solving this. Does it involve inversing?
     
  2. jcsd
  3. Oct 25, 2007 #2

    Dick

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    You are saying Bx=By. What's B(x-y)? Does that give you a hint?
     
  4. Oct 25, 2007 #3
    So, It's B(-2 -1)[tex]^{T}[/tex]

    I don't get it though. That doesn't look like a determinant.
     
  5. Oct 25, 2007 #4

    Dick

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    It's also equal to zero since Bx=By. It's not a determinant. But Bz=0 where z is a nonzero vector. What can that tell you about the determinant of B?
     
  6. Oct 25, 2007 #5
    That the determinant is 0 ?
     
  7. Oct 25, 2007 #6

    Dick

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    Yessssss.
     
  8. Oct 25, 2007 #7
    How do we know B(x) = 0?
     
  9. Oct 25, 2007 #8
    Ah nvm I see.

    Thanks for the help
     
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