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Does the 0 vector not count when determining the dimension?

  1. Oct 25, 2011 #1
    1. The problem statement, all variables and given/known data
    If we have ker(T)={0}, why is the dim(ker(T)) = 0?

    Does the 0 vector not count when determining the dimension? I thought the answer would be 1.
     
  2. jcsd
  3. Oct 25, 2011 #2

    Dick

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    Science Advisor
    Homework Helper

    Nope, doesn't count. The zero vector is in any vector space. Even a one-dimensional space has the zero vector in it. The zero vector isn't what makes it one-dimensional.
     
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