Determine whether the given set, together with the specified operations of addition and scalar multiplication, is a

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Determine whether the given set, together with the specified operations of addition and scalar multiplication, is a vector space. If it is not, list all of the axioms that fail to hold.

R2, with the usual scalar multiplication but addition defined by
A-A-A ху + x, + 1 Lyi + y½ + 1 X2

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