anonymous
  • anonymous
Can someone help me prove a property of vectors
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Prov ethat cu is a vector in R^n
anonymous
  • anonymous
c is a scaler and u is a vector
anonymous
  • anonymous
imagine c is\[ai+bj\] if we multiply it in c in the end we have a vector

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

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