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Homework Help: What is the dimension of its kernel?

  1. Jun 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Suppose that dim V = m and dim W = n with M>=n . If the linear map A : V -> W is onto, what is the dimension of its kernel?

    2. Relevant equations

    3. The attempt at a solution
    Onto, means that every vector in W has at least one pre-image therefore, the kernel can have a maximum dimension of m?
  2. jcsd
  3. Jun 8, 2009 #2


    Staff: Mentor

    Re: Kernel

    There is a property that you can use: dim(ker A) + dim(im A) = dim V. (see http://en.wikipedia.org/wiki/Kernel_(linear_operator [Broken])) The fact that A is onto W tells you something about dim(im A), the dimension of the image of A.
    Last edited by a moderator: May 4, 2017
  4. Jun 8, 2009 #3
    Re: Kernel

    ohhhhh is it m - n?
  5. Jun 8, 2009 #4


    User Avatar
    Science Advisor
    Homework Helper

    Re: Kernel

    Very likely it is.
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