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Math Help - rank nullity and linear transformation

  1. #1
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    Question rank nullity and linear transformation

    Hi So i am getting to the end of the material , and again I find one of the assignments I am supposed to understand saying left to the reading

    I really would like to see the proof to this a it would be really helpful

    rank nullity and linear transformation-mathforum.jpg
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  2. #2
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    Re: rank nullity and linear transformation

    do you know the rank-nullity theorem?
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  3. #3
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    Re: rank nullity and linear transformation

    Yes it's
    rank A + nullity A = n
    Where n is the Number of col
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Re: rank nullity and linear transformation

    Correct, now plugging in \text{rk}(A)=\text{null}(A) to the rank-nullity theorem gives n=2\text{rk}(A).
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