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Vector Spaces and Subspaces
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Which of the following is a vector space over the field of real numbers?
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A
The set of all ordered pairs of real numbers
💡 Explanation:
A vector space over a field F is a non-empty set V together with two operations, vector addition and scalar multiplication, that satisfy certain axioms. The set of all ordered pairs of real numbers, denoted by R^2, forms a vector space over the field of real numbers because it satisfies all the axioms of a vector space.