## Question

###### Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail. The set of all pairs of real numbers of the form $(x, y),$ where $x \geq 0,$ with the standard operations on $R^{2}$

Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail. The set of all pairs of real numbers of the form $(x, y),$ where $x \geq 0,$ with the standard operations on $R^{2}$

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