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Determine whether the following sets define vector spaces over R: (a) A={x∈R:x=k^2,k∈R} (b) B={x∈R:x=k^2,k∈Z} (c) C...

Determine whether the following sets define vector spaces over R:

  1. (a) A={x∈R:x=k^2,k∈R}

  2. (b) B={x∈R:x=k^2,k∈Z}

  3. (c) C ={p∈P^2 :p=ax^2,a∈R}

  4. (d) D={z∈C:|z|=1}

  5. (e) E={z∈C:z=a+i,a∈R}

  6. (f) F ={p∈P^2 : d (p)∈R}

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