1. Feb 22, 2007 #1

   Tonyt88

   

   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
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3. Feb 23, 2007 #2

   gammamcc

   

   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

   

   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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