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Vector Spaces

  1. Dec 7, 2007 #1


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    Let u and v be (fixed) vectors in the vector space V. Show that the set W of all linear combinations au+bv of u and v is a subspace of V.

    I cannot prove the above proof properly. Can anyone help.

  2. jcsd
  3. Dec 7, 2007 #2


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    Take two vectors from W, and show that their linear combination is also in W.
  4. Dec 7, 2007 #3


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    "Take two vectors from W" means taking two linear combinations, perhaps with different "a" and "b', say au+ bv and cu+ dv. "Their linear combination" would be something like x(au+ bv)+ y(cu+ dv) for numbers, x and y. "Show it is also in W" means "show it satisfies the definition of W". Here that means show that it also can be written au+ bv for some choices of a and b.
  5. Dec 8, 2007 #4


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    Thanks i understand it now
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