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Math Help - what is the dimension of the range

  1. #1
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    what is the dimension of the range

    T:R^n-->R defined by Tx=c1x1+...+cnxn..where atleast one of the c's is nonzero and x is in R^n..
    then what is the dimension of image(T)?
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  2. #2
    MHF Contributor

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    Since this is a function to R, the dimension of the range is at most 1. Since "at least one of the c's is nonzero" T does not map every vector to 0 so the dimension of the range is at least 1.
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