Let V be the set of all pairs (x, y) of real numbers and let F be the field of real
numbers. Define (x1, y1
) + (x2, y2
) = (x1, y1
) and k (x1, y1
) = (k x1, k y1
)
∀ (x1, y1
), (x2, y2
) ∈ V and k ∈ F
Examine with these operations whether V is a vector space over the field of real number or not ?
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Answer:
No, V is not a vector space over the field of real number.
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