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Linear independence and decompostion

  1. Oct 4, 2011 #1
    Explain why the method of decomposition when applied to the solution set of a homogeneous linear system always yields a linearly independent set of vectors whose span is the set of solutions....

    Can someone explain this it seems reasonable but I can't seem to prove it to myself
  2. jcsd
  3. Oct 5, 2011 #2
    Maybe dependent spans do not exist because if that were to be the case the dependence would work itself out in the rref as a definite solution removing the dependence. So only independent spans form....

  4. Oct 6, 2011 #3
    Maybe if you explain to us what the method is, we can help you better, and, in doing the explaining, you may understand things better yourself.
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