Question: Example 4. Let F be a field. Then the set Fn = {(a1, a2, ... di) ..., an) : a; EF} forms a vector space

Example 4. Let F be a field. Then the set Fn = {(a1, a2, ... di) ..., an) : a; EF} forms a vector space over F w.r.t. addition and scalar multiplication defined as follows. If x = (a1, a2, ...., an), y = (b1, b2, ..., bn) E Fn, then x ty = (a1 + b1, a2 + b2, ...., an + bn) and if a is any element of F, then ax = (ac1, ad2, ...., aan)

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