Question

Can anyone help me prove proerties of vectors?

Answer 1

prove that u+v is a vector in R^n

Answer 2

u=(u1,...,un), v=(v1,...vn)=>u+v=(u1+v1,...un+vn)
since each vector has real coordinates and the sum of two real numbers is a real number (closure property) it follows u+v in Rn

Answer 3

Hey that was awesome. LOL stick around I have 10 properties to prove and I suck at proving

Answer 4

umm I have another one lol

Answer 5

u+v=v+u and we r disussing vectors in r^n

Answer 6

True, because of the commutativity property of real numbers (following the previous line of reasoning)

Answer 7

ya but i have to prove it and like how wld i do that

Answer 8

u=(u1,...,un), v=(v1,...vn)=>u+v=(u1+v1,...un+vn)
v+u=(v1+u1,...vn+un)
for each k, uk+vk=vk+uk (in real numbers) because of commutativity
So u+v=v+u

Answer 9

Thanks :D

Answer 10

welcome :)

Answer 11

I need help with another one but maaybe i will do it another post so i can give u more medals :D

Answer 12

Not that interested in medals ... :) but you should try them for yourself...
I should show you how to fish, not to fish in your place ...:)

Answer 13

heehe

Answer 14

lol i am figuring this one out on my own :D

Answer 15

:) maybe you should put the question in the form "is this correct?"

Answer 16

hehe ya i will do that for the next one :D

Answer 17

I did like 4 on my own :D lol

Answer 18

but now I am stuck
Prove that cu is a vector in R^n

Answer 19

u=(u1,...,un), c in R, then
cu=(cu1,...,cun), vector because the multiplication of two real numbers is a real number