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Math Help - Subspaces & spans

  1. #16
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    By using Gauss method you should leave the first line intact (after choosing the good one) and use it to eliminate the others when you done,you passe to the second line and use it to eliminate the rest and so on.
    .. and that's what you didn't
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  2. #17
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  3. #18
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    Quote Originally Posted by Raoh View Post
    By using Gauss method you should leave the first line intact (after choosing the good one) and use it to eliminate the others when you done,you passe to the second line and use it to eliminate the rest and so on.
    .. and that's what you didn't

    cool thanks, I see the error of my ways now...

    1 last question though, how does the equation that i derive from gauss method show that the set spans R3?
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  4. #19
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    ok,suppose we have \frac{2}{3}x+\frac{5}{3}y-z=0.
    \vec{x}=(x,y,z)\in span(\left ( 1,2,4 \right ),\left ( 2,1,3 \right ),\left ( 4,-1,1 \right ))
    if and only if (-\frac{5}{2}y+\frac{3}{2}z,y,z)= \alpha_{1}(1,2,4) + \alpha _{2}(2,1,3) + \alpha _{3}(4,-1,1)
    which leads us to another system of equations.
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  5. #20
    Junior Member SirOJ's Avatar
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    Quote Originally Posted by Raoh View Post
    ok,suppose we have \frac{2}{3}x+\frac{5}{3}y-z=0.
    \vec{x}=(x,y,z)\in span(\left ( 1,2,4 \right ),\left ( 2,1,3 \right ),\left ( 4,-1,1 \right ))
    if and only if (-\frac{5}{2}y+\frac{3}{2}z,y,z)= \alpha_{1}(1,2,4) + \alpha _{2}(2,1,3) + \alpha _{3}(4,-1,1)
    which leads us to another system of equations.

    Thanks alot , sorry if it took me a bit of time to get my head around it..
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  6. #21
    Junior Member SirOJ's Avatar
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    Acutually Raoh if your still around, would you be so kind as to answer another question..(dont see the point in starting a new thread)

    It's about linear transformations

    (b) Let
    L : R3 ->R2 be the linear transformation defined by

    L
    (x, y, z) = (x y, y z)

    (i) Find the standard (2
    3) matrix representation of L and compute L(1, 1, 1).

    I know how to show something is a linear transformation but unsure how to start this question. Just the starting point is all i'm looking for. Maybe i've wasted too much of your time already...
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  7. #22
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    Quote Originally Posted by SirOJ View Post
    Acutually Raoh if your still around, would you be so kind as to answer another question..(dont see the point in starting a new thread)

    It's about linear transformations

    (b) Let
    L : R3 ->R2 be the linear transformation defined by

    L
    (x, y, z) = (x y, y z)

    (i) Find the standard (2
    3) matrix representation of L and compute L(1, 1, 1).

    I know how to show something is a linear transformation but unsure how to start this question. Just the starting point is all i'm looking for. Maybe i've wasted too much of your time already...
    i would be glad to answer your question but it's beyond my level.
    you can start another thread,others certainly will answer you.
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