# Vector Spaces Question

mpm
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

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

Any help would be greatly appreciated.

mpm

Last edited:

This is an epsilon ($\epsilon$), you're looking for a different symbol, the "is a member or element of" relation ($\in$). So you have:
$$(\mathbb{R}^+, \oplus, \otimes)$$
with the following definitions, for all x, y in R+ and all scalars (reals) $\lambda$:
$$x \oplus y = x \times y$$
$$\lambda \otimes x = x^{\lambda}$$