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anonymous

  • 5 years ago

Anyone good with vector spaces?

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  1. anonymous
    • 5 years ago
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    a collection of vectors that contains theta must be linearly dependent. Thus theta cannot be contained in a basis. How do you go about proving this? I know that

  2. anonymous
    • 5 years ago
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    ...I know that to be linearly dependent there must be scalars that are not zero in the collection of vectors, Does theta mean zero, or some sort of value?

  3. anonymous
    • 5 years ago
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    ...theta is also zero...and the collection of vectors must = zero in the end

  4. helpmeplease
    • 5 years ago
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    You have to prove some axioms regarding vector spaces. Suppose you had \[\{R^2= <x,y> | x,y \in R\}\] Define Addition as: \[ <x_1,y_1> + <x_2,y_2> = <x_1+x_2,y_1+y_2>\] Then: \[ <x_1,y_1> + <x_2,y_2> = <x_1+x_2,y_1+y_2>=<a,b>\] \[\in R= <x,y>\] Therefore, closed under addition, since the addition of two elements = an element inside \[R^2\]. Rinse and repeat for the other ones.

  5. anonymous
    • 5 years ago
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    thanks a lot

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