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Math Help - null,dimension exam approaching!!

  1. #1
    n22
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    null,dimension exam approaching!!

    Hi!
    Please help me solve:
    Suppose that A and B are mxn matrices
    (i)Using dimension thm(or otherwise)show that Null(A)=R^n if and only if A=0
    ii)Using (i)(or otherwise)prove that A=B if and only if Ax=Bx for all x is an element of R^n

    Thanks.
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  2. #2
    MHF Contributor
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    Re: null,dimension exam approaching!!

    I am not sure about the dimension theorem, but if a matrix has a non-zero element, it is easy to write a vector that, when multiplied by the matrix, gives a non-zero vector. Point ii) follows immediately from i).
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