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Theoretic or vector notation

  1. Jan 8, 2004 #1
    I am having a hard time with this problem, and i need some help.

    It says:
    In Exercisies 11-17, use set theoretic or vector notation or both to describe the points that lie in the given configurations.

    11.) The plane spanned by v1 = (2,7,0) and v2 = (0,2,7)

    In the back of the book they have this answer
    {(2s,7s+2t,7t)| sER, tER}

    I know all they did was add the two vectors together, but i dont know how the got s, and t and what they represent.

    E= is a member of
     
  2. jcsd
  3. Jan 8, 2004 #2
    A vector is in the span of v1 and v2 if and only if it is a linear combination of v1 and v2. In other words, v is in the span if

    [tex]\boldsymbol{v}=s\boldsymbol{v}_1+t\boldsymbol{v}_2[/tex]

    where s and t are any two real numbers. This is pretty much what the set theory notation is saying.


    Perhaps I didn't explain this too well. I'm not sure what your level of knowledge is, so I don't know how in-depth you need me to go.
     
    Last edited: Jan 8, 2004
  4. Jan 9, 2004 #3

    HallsofIvy

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    Looks good to me master_coda.

    Rajvirnijjar, perhaps you should review the concept of "spanning".
     
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