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I have a homework problem that I can't figure out and there is nothing in the book that helps me out. I was hoping someone could shed some light.

Let R^+ denote the set of postive real numbers. Define the operation of scalar muplication, denoted * (dot) by,

a*x = x^a

for each X (episilon) R^+ and for any real number a. Define the operation of addition, denoted +, by

x + y = x * y for all x, y (Epsilon)R^+

Thus for this system teh scalar product of -3 times 1/2 is given by

- 3 * 1/2 = (1/2)^-3 = 8

and the sume of 2 and 5 is given by

2 + 5 = 2 * 5 = 10

Is R^+ a vector space with these operations? Prove your answer.

The plus should be a plus with a circle around it but I couldnt figure out how to put it in there. Im also not sure how to make the epsilon either.

Any help would be greatly appreciated.

mpm

Let R^+ denote the set of postive real numbers. Define the operation of scalar muplication, denoted * (dot) by,

a*x = x^a

for each X (episilon) R^+ and for any real number a. Define the operation of addition, denoted +, by

x + y = x * y for all x, y (Epsilon)R^+

Thus for this system teh scalar product of -3 times 1/2 is given by

- 3 * 1/2 = (1/2)^-3 = 8

and the sume of 2 and 5 is given by

2 + 5 = 2 * 5 = 10

Is R^+ a vector space with these operations? Prove your answer.

The plus should be a plus with a circle around it but I couldnt figure out how to put it in there. Im also not sure how to make the epsilon either.

Any help would be greatly appreciated.

mpm

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