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Linear tranformations equality

  1. Nov 28, 2009 #1
    1. The problem statement, all variables and given/known data

    We are given a homogeneous system of 5 equations and 3 variables. We are asked to find the solutions (which i found to be unique and <0,0,0>) and then we are asked(along loads of other stuff:P):

    a)If any two linear transformations g and f have kerf=kerg=<0,0,0> then they are equal.
    b)If any two linear transformations g and f have imf=img=<0,0,0> then they are equal.

    2. Relevant equations



    3. The attempt at a solution

    a) is wrong because there are infinite linear transformations with ker=<0,0,0> but different images. for (positive but not absolutely sure i am correct because the dimension of the images would be equal)
    i think b) is correct but i am not sure. I would say that if imf=img=<0,0,0> then they are both the zero linear map so they are equal. Thanks again in advance
     
  2. jcsd
  3. Nov 28, 2009 #2
    Sounds to me like you've got it down!
     
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