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Give an example of a linear transformation

  1. Feb 22, 2007 #1

    Tonyt88

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    1. The problem statement, all variables and given/known data
    Give an example of a linear transformation whose kernel is the line spanned by:

    -1
    1
    2

    in lR³

    2. Relevant equations



    3. The attempt at a solution

    Would:

    1..(-1)...0
    0....0.....0
    0..(-2)...1

    be a solution?
     
    Tonyt88, Feb 22, 2007
  2. jcsd
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  3. Feb 23, 2007 #2

    gammamcc

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    To prove it, prove your vector is in the kernel and that the dimension of the col. space is 3 - nullity = 2.
     
    gammamcc, Feb 23, 2007
  4. Feb 23, 2007 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    It quite obviously isn't since Av is not 0. Are you clear on the definition of "kernel"?

    Actually your matrix has only a single entry wrong so it may be just a typo.
     
    HallsofIvy, Feb 23, 2007
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