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Quick Linear Algebra-True or false type

  1. Nov 3, 2008 #1
    Quick Linear Algebra---True or false type

    1. The problem statement, all variables and given/known data

    If A is a m*n matrix and B is a n*n matrix, does nullity AB= nullity A* nullity B?

    I think that it does, but I am not sure. I don't need a proof of this or anything, this is just a fact I need to know in order to try and prove something more complicated.
  2. jcsd
  3. Nov 3, 2008 #2


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    Re: Quick Linear Algebra---True or false type

    Are you sure null(A)*null(B) is always small enough to be equal to null(AB)? Try, e.g. m=n=3 and see if you can get null(A)=null(B)=2

    If you're stuck, check the spoiler

    For an even more trivial case, m=n=2, A=B=0 the zero matrix.
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