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Linear Algebra Proof

  1. Oct 11, 2005 #1
    Hi,

    There is an example of this question in the book but I cannot understand the part where it says 2AT = 2[2AT]T. Everything else I understand. (T means Transpose)

    Suppose a square matrix A satisfies A = 2AT. Show that necessarily A=0.

    A = 2AT = 2[2AT]T = 2[2(AT)T] = 4A

    3A = 0
    A=1/3(3A) = 1/3(0) = (0)


    Thanks!
     
  2. jcsd
  3. Oct 11, 2005 #2
    They are just using the assumption [itex]A = 2A^T[/itex] in that step.
     
  4. Oct 11, 2005 #3
    I think I get it. So basically are they doing that step to get rid of the Transpose so A will be alone, and then can be isolated?

    Thanks
     
  5. Oct 11, 2005 #4
    Yes, you could say that. :smile:
     
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