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Solve the following problems using the concepts and notation of set theory and vector spaces: What is...

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Advance Math

Solve the following problems using the concepts and notation ofset theory and vector spaces:

  1. What is a Cartesian vector?
  2. What is a real vector space?
  3. Does the rational numbers fulfill the definition of afield?
  4. Define linearly dependency for any set of vectors.
  5. Assess the linearly dependency (or not) of the followingvectors: u=<2,-1,1>,v=<3,-4,-2>, and w=<5,-10,-8>
  6. Define basis

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