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Homework Help: Please help. What is the relation between the kernel of A an

  1. Feb 20, 2015 #1
    1. The problem statement, all variables and given/known data
    1. What is the relation between the kernel of A and the kernel of (A^2 + A)?
    2. Relevant equations


    3. The attempt at a solution

    Break into A^2x = 0 and Ax = 0. We know Ax = 0 because that's the kernel of A, ker(A^2x) is subset of ker(A) so ker(A^2 + A) is a subset of ker (A)????
     
  2. jcsd
  3. Feb 20, 2015 #2

    PeroK

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    Why not start with ##x \in ker(A)## and start from there? You need to formalise your answer. You've got an outline for the answer, but you need to sharpen your logic.
     
    Last edited: Feb 20, 2015
  4. Feb 20, 2015 #3

    HallsofIvy

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    In both this and the previous question about image, it is useful to note that [itex]A^2+ A= A(A+ I)= (A+ I)A[/itex].
     
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