Determine whether the 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 real numbers x with the standard operations of addition and multiplication.

Determining whether the set equipped with the given operation is a vector space is that Under the standard operations of Multiplication and addition, the set of all real numbers follows the additive inverse, closure, associative, distributive, and identity element properties. It also follows the usual distributive laws. Therefore R is a vector space.