Can someone help me prove a property of vectors

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Can someone help me prove a property of vectors

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Prov ethat cu is a vector in R^n
c is a scaler and u is a vector
imagine c is\[ai+bj\] if we multiply it in c in the end we have a vector

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ummm my prof wldnt accept that
hence vector have dirction & magnitude so cu it has too characteristic get it? could i explain well?
ya pretty good :D
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 \( \mathbb{R}^n \).
thnx friend
yup that is what i was looking for :D
Thanks guys :D I still need to prove 4 more properties so I may be back
jamsj answer is better than mine Pippa
Imitate the method here then. Show explicitly that the resulting quantity meets exactly the definition required. good luck.
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

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