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owlet

  • one year ago

How to determine whether a set of vectors is subspace of R^n or not? I'm confused about this topic.

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  1. owlet
    • one year ago
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    they said I have to satisfy two conditions but Idk how to apply it

  2. amistre64
    • one year ago
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    how do you define 'subspace'. what properties do we look for?

  3. owlet
    • one year ago
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    like for example I have this question in a book that says it is not a subspace. |dw:1443912367126:dw|

  4. owlet
    • one year ago
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    subspace of R^2 for that problem^

  5. owlet
    • one year ago
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    It says here... there are rules that must be satisfied to know if something is a subspace of R^2: \[x + y \in S\\ tx \in S\] x and y are vectors

  6. Jhannybean
    • one year ago
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    So basically what factors define an area of R\(^2\) ?

  7. amistre64
    • one year ago
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    so closed under addition and scalar multiplication

  8. owlet
    • one year ago
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    I guess so..?

  9. amistre64
    • one year ago
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    is -(x1,x2) in the vector space?

  10. owlet
    • one year ago
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    I'm guessing no? because x1 and x2 should be greater than 0?

  11. amistre64
    • one year ago
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    thats what im thinking to and there is no restriction in the value of our scalar is there?

  12. amistre64
    • one year ago
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    (-x1, -x2) is not in the defined set

  13. owlet
    • one year ago
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    So it means, I just have to check the conditions in the given set if they follow those two rules? If they don't follow it, then it is not a subspace? am i understanding it right?

  14. amistre64
    • one year ago
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    correct, if the properties are not satisfied in order to be defined as something, then we cannot claim that it exists as that thing.

  15. amistre64
    • one year ago
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    calling a cat a tree, is not valid logic is it :)

  16. owlet
    • one year ago
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    lol okay, I think I get it now, thank you! :D

  17. amistre64
    • one year ago
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    good luck

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