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Linear Algebra problem

  1. Jan 11, 2009 #1
    Hello !
    i try to solve Linear algebra question(but need be written properly as mathmatical proofs)
    Having A matrice nXn:
    1)proove that if A^2=0 the columns of matrice A are vectors in solution space of the system Ax=0 (x and 0 are vectors of course),and show that p(A)>=n/2
    2)proove that if p(A^2)<p(A) (p in all cases here means: the rank of the vectors)
    so the system Ax=o has a non trivial solution and the System A^2x=0 has solution y which is Ay≠0,,,,
    I have the general clue but how write it right,math way i have big problem..
    thank you very much
  2. jcsd
  3. Jan 11, 2009 #2


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    Science Advisor

    What is A(1, 0, 0...)T? A(0, 1, 0,...)T?, etc.

    vectors don't have "ranks". I presume you mean the rank of A2 and A.

    If you have a "general clue" please tell us what it is. Perhaps we can help with the mathematics notation for that. I started to give a hint but I suspect it may be just your "general clue".
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