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Composition of linear transformations

  1. Oct 25, 2011 #1
    1. The problem statement, all variables and given/known data

    Find two linear operators T and U on R^2 such that TU = 0 but UT ≠ 0.

    3. The attempt at a solution

    Let T(x1,x2)=(0,x2)

    Let U(x1,x2)=(x2,0)



    TU(x1,x2)=T(x2,0)=(0,0)

    Am I right?

    'Cause I can't remember if TU(x1,x2)=T[U(x1,x2)]

    Or TU(x1,x2)=U[T(x1,x2)]
     
  2. jcsd
  3. Oct 25, 2011 #2
    Looks good to me!!

    And it's indeed

    [tex](TU)(x)=T(U(x))[/tex]
     
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