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Is the trivial solution a unique solution?

  1. Aug 1, 2010 #1
    If the only solution to Ax = b is the trivial solution, then is that solution considered unique?
     
  2. jcsd
  3. Aug 1, 2010 #2

    Office_Shredder

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    If b is non-zero, there is no trivial solution.

    If b is zero, and A is invertible, then yes, x=0 is the unique solution
     
  4. Aug 1, 2010 #3
    Do you know how to tell if the least squares approximation exists?
     
  5. Aug 2, 2010 #4
    If it's the only solution, then by definition it's unique.
     
  6. Aug 2, 2010 #5

    HallsofIvy

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    It doesn't matter whether it is trivial or not, "only solution"= "unique solution".

    I have no idea what "Do you know how to tell if the least squares approximation exists?" has to do with "unique solutions" but approximations, whether good or bad, always exist.
     
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