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Homework Help: Matrix groups

  1. Jan 31, 2008 #1
    1. The problem statement, all variables and given/known data

    http://img88.imageshack.us/img88/3148/scan0001ba3.th.jpg [Broken]

    2. Relevant equations

    3. The attempt at a solution

    I have done part a, proving the four axioms. I just dont understand part b) if someone could point me in the right direction...
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Jan 31, 2008 #2


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    Suppose g=[a b,0 d] (I hope the informal matrix notation is clear) is in the center. That means for ANY g'=[a' b',0 d'] in the group, that g*g'=g'*g. Write that out in components. You should find a*b'+b*d'=a'*b+b'*d. Now since the primed components are arbitrary, what does this imply for g if you pick say, a'=1, b'=0 and d'=0. Or if you pick a'=0, b'=1 and d'=0???
  4. Feb 1, 2008 #3
    a = d , b = 0 ?
  5. Feb 1, 2008 #4
    ...so Z(G) = ( a 0 ,0 a ) ?
  6. Feb 1, 2008 #5


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    Does that say "Z(G)= {g | gh= hg for all h}"? The lower bar of the "=" is very pale and it looks like "gh- hg" which makes no sense!
  7. Feb 1, 2008 #6
    yes it does - strange though, shows up fine on my screen
  8. Feb 1, 2008 #7
    a quick reply would be much appreciated as i have to hand this in pretty soon
  9. Feb 1, 2008 #8


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    Yes, the center is the multiples of the identity.
    Last edited: Feb 1, 2008
  10. Feb 1, 2008 #9
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