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anonymous

  • 4 years ago

Can someone help me prove a property of vectors

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  1. anonymous
    • 4 years ago
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    Prov ethat cu is a vector in R^n

  2. anonymous
    • 4 years ago
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    c is a scaler and u is a vector

  3. anonymous
    • 4 years ago
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    imagine c is\[ai+bj\] if we multiply it in c in the end we have a vector

  4. anonymous
    • 4 years ago
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    ummm my prof wldnt accept that

  5. anonymous
    • 4 years ago
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    hence vector have dirction & magnitude so cu it has too characteristic get it? could i explain well?

  6. anonymous
    • 4 years ago
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    ya pretty good :D

  7. JamesJ
    • 4 years ago
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    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
    • 4 years ago
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    thnx friend

  9. anonymous
    • 4 years ago
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    yup that is what i was looking for :D

  10. anonymous
    • 4 years ago
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    Thanks guys :D I still need to prove 4 more properties so I may be back

  11. anonymous
    • 4 years ago
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    jamsj answer is better than mine Pippa

  12. JamesJ
    • 4 years ago
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    Imitate the method here then. Show explicitly that the resulting quantity meets exactly the definition required. good luck.

  13. anonymous
    • 4 years ago
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    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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