Let V = Z be the set of integers with the usual addition as “vector addition.”
Show that it is not possible to define scalar multiplication by Q;R; or C so as to
make it into a vector space.

Question

Let V = Z be the set of integers with the usual addition as “vector addition.”
Show that it is not possible to define scalar multiplication by Q;R; or C so as to
make it into a vector space.

anonymous · Answer

What IS scalar multiplication as required by vector spaces anyway? :D

anonymous · Answer

$$(\alpha f)(x) = \alpha f (x) $$

anonymous · Answer

(f1 + f2)(x) = f1(x) + f2(x)

anonymous · Answer

Yes, well, some key property of scalar multiplication is off...

anonymous · Answer

im not sure i understand what you mean

anonymous · Answer

Well, it's asking you why you can't define scalar multiplication by scalars from Q, R, and C.

What is scalar multiplication?

anonymous · Answer

okay okay i think i get it thank you :)

anonymous · Answer

Good. :)