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PRO/VS-02008
Consider the set of all vectors \(\xi=(\xi_1,\xi_2,\xi_3)\) in \(C^3\) for
which

  1. \(\xi_1\) is real
  2. \(\xi=0\)
  3. \(|\xi_1|> 0\)
  4. either \(\xi_1\) or \(\xi_2\) equal to zero
  5. \(\xi_1+\xi_2=0\)
  6. \(\xi_1+\xi_2=1\)


Give the dimensions of the vector spaces, wherever appropriate and give a
possible basis

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4727:Diamond Point

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