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Homework Help: Proper format for writing basis in linear algebra

  1. Jan 27, 2009 #1
    if i am asked to find a basis for a vector subspace, am i meant to jus write one possible option, for example

    basis: (8,0,0)(0,6,0)(0,0,2)

    or am i supposed to write the whole span

    basis: sp{(8,0,0)(0,6,0)(0,0,2)}

    or am i meant to write it with parameters

    basis: a(8,0,0) + b(0,6,0) + c(0,0,2)

    or am i meant to write it in its simplist form

    basis: (1,0,0)(0,1,0)(0,0,1)


    and how about when i am asked to present all possible basises
     
  2. jcsd
  3. Jan 27, 2009 #2

    CompuChip

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    The basis is a set which consists of three vectors, so I would write:
    B = { (8,0,0), (0,6,0), (0,0,2) }
    just like you would write set of three numbers like S = {1, 6, 12}.
    If you want to give a normalized basis (or that is asked of you), you can write
    [itex]\hat B[/itex] = { (1, 0, 0), (0, 1, 0), (0, 0, 1) }

    The vector space V which is spanned by that basis is denoted by
    V = sp(an) B = sp( { (8,0,0), (0,6,0), (0,0,2) } )
    which means that you can write an arbitrary vector v in V as a linear combination
    a(8,0,0) + b(0,6,0) + c(0,0,2)

    Is that clear?
     
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