Question

Can someone help me prove a property of vectors

Answer 1

Prov ethat cu is a vector in R^n

Answer 2

c is a scaler and u is a vector

Answer 3

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

Answer 4

ummm my prof wldnt accept that

Answer 5

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

Answer 6

ya pretty good :D

Answer 7

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 \( \mathbb{R}^n \).

Answer 8

thnx friend

Answer 9

yup that is what i was looking for :D

Answer 10

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

Answer 11

jamsj answer is better than mine Pippa

Answer 12

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

Answer 13

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