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I need a step by step answer 2. Determine whether the set of all triples of real numbers with addition defined by (x, y, z)

I need a step by step answer

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2. Determine whether the set of all triples of real numbers with addition defined by (x, y, z) + (u, v,w) = (z+ w, y + v, x + u) and standard scalar multiplication is a vector space. If it is not a vector space, identify the vector space axioms that fail

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