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Let V be a 5 dimensional vector space

  1. May 26, 2005 #1
    Let V be a 5 dimensional vector space, and let [tex]\Delta[/tex] be a determinant formon V. Given [tex]\Delta[/tex](b1, b2, b3, b4, b5)= -3

    How do I find [tex]\Delta[/tex](b4, b3, b5, b1, b2)?
     
  2. jcsd
  3. May 26, 2005 #2

    mathwonk

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    use properties of determinnats, i.e. interchanging two rows changes the determinant by a minus sign. did you know this? if not, go back and review what properties determinants have.

    or let me just tell you:

    a determinant is an
    1) alternating
    2) multilinear
    3) normalized

    function of n variables, where n = dim(V).

    normalized means that if there is some preferred basis, like e1,....,en, then det(e1,...,en) = 1.

    more intrinsically, if it is only defined for endomorphisms, then det(Id) = 1.
     
    Last edited: May 26, 2005
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