## anonymous 4 years ago Can someone help me prove a property of vectors

1. anonymous

Prov ethat cu is a vector in R^n

2. anonymous

c is a scaler and u is a vector

3. anonymous

imagine c is$ai+bj$ if we multiply it in c in the end we have a vector

4. anonymous

ummm my prof wldnt accept that

5. anonymous

hence vector have dirction & magnitude so cu it has too characteristic get it? could i explain well?

6. anonymous

ya pretty good :D

7. JamesJ

As $$u \in \mathbb{R}^n$$ we can write $$u$$ as $u = (x_1, x_2, ..., x_n)$ where each of the $$x_i$$ are real numbers. Now by definition of scalar multiplication, $cu = (cx_1, cx_2, ..., cx_n)$ As each $$x_i$$ is a real number as is $$c$$, each component $$cx_i$$ is also a real number. Hence $$cu$$ is an $$n$$-tuple of real numbers and therefore a member of $$\mathbb{R}^n$$.

8. anonymous

thnx friend

9. anonymous

yup that is what i was looking for :D

10. anonymous

Thanks guys :D I still need to prove 4 more properties so I may be back

11. anonymous

jamsj answer is better than mine Pippa

12. JamesJ

Imitate the method here then. Show explicitly that the resulting quantity meets exactly the definition required. good luck.

13. anonymous

Thanks james I finished all the proving :D On my own which is a big feat for me. I think I am getting the hang of it