Let be the set of positive real numbers, let = and = be any vectors (i.e., positive real numbers) in , and let be any scalar. Define the operations on to be = [Vector addition is numerical multiplication.] = [Scalar multiplication is numerical exponentiation.] Prove axioms 4 and 5 for this vector space. (Find the identity vector and the inverse of each vector.)

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usama1632000 usama1632000

09-06-2024
Mathematics

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Let be the set of positive real numbers, let = and = be any vectors (i.e., positive real numbers) in , and let be any scalar. Define the operations on to be = [Vector addition is numerical multiplication.] = [Scalar multiplication is numerical exponentiation.] Prove axioms 4 and 5 for this vector space. (Find the identity vector and the inverse of each vector.)

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