Thread: Vector Space question
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Old June 20th, 2008, 01:44 PM
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Consider vectors: \bold{u} = (1, u_{2}, u_{3}) and \bold{v} = (1, v_{2}, v_{3}).

One of the axioms state that if u and v are vectors in your vector space, then so should u + v. However:
\bold{u} + \bold{v} = (2, u_{2} + v_{2}, u_{3} + v_{3})

which does not belong in your vector space.
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