Consider R with standard addition, that is, r⊕s=r+s, but with the nonstandard scalar multiplication k⊗r=k2r. Prove that at least one vector space axiom holds true and at least one vector space axiom fails.

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25-06-2024
Mathematics

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Consider R with standard addition, that is, r⊕s=r+s, but with the nonstandard scalar multiplication k⊗r=k2r. Prove that at least one vector space axiom holds true and at least one vector space axiom fails.

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