Determine whether the set equipped with the given operations is a vector space. For those that...

 

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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 n-tuples of real numbers of the form (x, x,...,x) with the standard operations on R". V is not a vector space, and Axioms 7 and 8 fail to hold. V is not a vector space, and Axiom 8 fails to hold. V is not a vector space, and Axioms 4 and 5 fail to hold. V is not a vector space, and Axioms 1 - 3 fail to hold. V is a vector space. 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 n-tuples of real numbers of the form (x, x,...,x) with the standard operations on R". V is not a vector space, and Axioms 7 and 8 fail to hold. V is not a vector space, and Axiom 8 fails to hold. V is not a vector space, and Axioms 4 and 5 fail to hold. V is not a vector space, and Axioms 1 - 3 fail to hold. V is a vector space.

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