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Help linear operator problem

  1. May 24, 2005 #1
    Let T: R^3 -> R^3 be a linear operator and
    T(x;y;z)= (x -y + 3z;2x-y+8z;3x -5y+5z).

    Find the rule, for the linear operator S: R^3 -> R^3 such that ker S= Im T and Im S=Ker T.

    I'm not really sure how I should start this problem. Also I would like to know if I can assume S is the inverse operator of T.
     
  2. jcsd
  3. May 24, 2005 #2

    Hurkyl

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    Seems obvious to me that the first thing to do is to find ker T and im T. *shrug*

    What do you think?
     
  4. May 25, 2005 #3

    HallsofIvy

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    " Also I would like to know if I can assume S is the inverse operator of T."

    If the two kernals are not trivial, then T does not HAVE an inverse!
     
  5. May 29, 2005 #4
    I found ker T and Im T and I'm still stuck. I know it's not the inverse operator but I still don't know how to find the rule for the linear operator S.
     
  6. May 29, 2005 #5

    Hurkyl

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    Maybe if you described them geometrically, it would spark an idea?
     
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