(8.1) Let F be a field. Prove, showing all the detail, for n ∈ N, that Fn with componentwise addition and componentwise
scalar multiplication, is a vector space over F.
(8.2) Let F be a field. Consider the set
V={(a1,a2,0) : a1,a2 ∈ F}.
Prove that V, together with the operations defined in (8.1) above, is a vector subspace of the vector space defined in (8.1).
Use the subspace theorem to prove this.
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