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Math Help - Vector

  1. #1
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    Vector

    *Choose two linearly independent vectors among the following vectors:
    , ,


    Extend them to a base in the room.*

    Idk if this progress is wrong but here what i thought
    (2,1,2)=y(0,0,2)+x(4,2,2) and i find that y = 1/2 and x = 1/2
    idk what to do or if this is right thinking
    Last edited by Petrus; November 19th 2012 at 12:46 PM.
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  2. #2
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    Re: Vector

    any1 know ?
    Last edited by Petrus; November 19th 2012 at 12:31 PM.
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  3. #3
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    Re: Vector

    Vector-mattehjalp1.jpg
    so on top it says Choose two linearly independent vectors among the following vectors:
    and at the next text it says Extend them to a base in the room.
    and svar means "answer"
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  4. #4
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    Re: Vector

    let's pick 2 and see if there are linearly independent. i'm lazy, so i'll just pick the first 2.

    now (4,2,2) and (0,0,2) are linearly independent if:

    a(4,2,2) + b(0,0,2) = (0,0,0) forces us to pick a = b = 0.

    now a(4,2,2) + b(0,0,2) = (4a,2a,2a) + (0,0,b) = (4a,2a,2a+b).

    if (4a,2a,2a+b) = (0,0,0) we have:

    4a = 0
    2a = 0
    2a+b = 0

    from 4a = 0 (or 2a = 0), we see we must have a = 0. then:

    2a+b = 0 becomes:

    0+b = 0
    b = 0, so we see (4,2,2) and (0,0,2) are, in fact, linearly independent.

    presumably, you mean extend {(4,2,2),(0,0,2)} to a basis for all of R3.

    to do this, we need a third vector NOT in span({(4,2,2),(0,0,2)}).

    so we need a vector NOT of the form (4a,2a,2a+b).

    can you think of one? (hint: pick a vector whose 2nd coordinate is not ____ of the first one).
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  5. #5
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    Re: Vector

    hi deveno
    im pretty new on vector and i keep read and search but dont get it :/ is it anyway i can draw this so i can find it more easy ?
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