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Math Help - how do u prove these claims?

  1. #1
    Senior Member
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    Feb 2008
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    how do u prove these claims?




    i think the first part, we can say that assume A represents a linear map  \alpha : V\longrightarrow W and dimV is greater than dimW. So alpha is surjective which means n(A) is nonzero.

    And k is the least number makes the linear map surjective, which means, dimV=dimW+1, and n(A)=1

    but i got no idea with (b) and etc.
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