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Math Help - subspace of V

  1. #1
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    subspace of V

    How do I verify that the following is a subspace of V?

    w=(x,y,2x-3y), x and y are real numbers. V=R^3

    I am stuck at how to set it up. This is what I think.

    (x,y,2x-3y)+?=

    I don't know what to add. I know that if w=(x,x1,x2), I can add that too (y,y1,y2). But what about (x,y,2x-3y)? Please help on how to set it up. Thank you
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by ephemeral1 View Post
    How do I verify that the following is a subspace of V?

    w=(x,y,2x-3y), x and y are real numbers. V=R^3

    I am stuck at how to set it up. This is what I think.

    (x,y,2x-3y)+?=

    I don't know what to add. I know that if w=(x,x1,x2), I can add that too (y,y1,y2). But what about (x,y,2x-3y)? Please help on how to set it up. Thank you
    (x,y,2x-3y)+(x',y',2x'-3y')=(x+x',y+y',2(x+x')-3(y+y'))
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  3. #3
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    Smile

    you don't have to verify each axiom,
    w=\left \{ x(1,0,2)+y(0,1,-3)\mid x,y\in \mathbb{R} \right \}
    =\texttt{Span}((1,0,2),(0,1,-3))
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