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Math Help - one-dimensional subspace of R^3

  1. #1
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    one-dimensional subspace of R^3

    Question:Give an example of a 1-dimensional subspace U of R3.

    Answer: Any line through the origin is a one-dimensional subspace of R3.

    How do i write this as a set? i mean U=?

    thanks
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  2. #2
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    Quote Originally Posted by charikaar View Post
    Question:Give an example of a 1-dimensional subspace U of R3.

    Answer: Any line through the origin is a one-dimensional subspace of R3.

    How do i write this as a set? i mean U=?

    thanks

    You should know this from analytic geometry: U=\{t\cdot (a,b,c)\,\mid\,\,t\in\mathbb{R}\,,\,(a,b,c)\neq (0,0,0)\} is a straight line through the origin in 3-dimensional space, which is EXACTLY the same as the span of one non-zero vector...

    Tonio
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  3. #3
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    a,b,c are all real?
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