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Math Help - Subspace of R3

  1. #1
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    Subspace of R3

    Determine weather w={(x,2x,3x): x a real number} is a subspace of R3
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  2. #2
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    To be a subspace it must confirm three axioms:

    Containing the zero vector, closure under addition and closure under scalar multiplication

    a) (0,0,0) is contained since (0,2*0,3*0)=(0,0,0)
    b) Let (y,2y,3y) be a vector, then (x,2x,3x)+(y+2y+3y)=(x+y,2(x+y),3(x+y)) => closure under addition
    c) Let c be a constant, then c*(x,2x,3x)=(cx, 2(cx), 3(cx)) => closure under scalar multiplication

    So it's a subspace. I hope this is what you wanted and that will help you!
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  3. #3
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    Quote Originally Posted by rabih2011 View Post
    Determine weather W={(x,2x,3x): x a real number} is a subspace of R3
    Notice that (0,0,0)\in \mathbb{R}^3. WHY?
    Suppose that \{a,b\}\subset W and \alpha\in\mathbb{R}.
    If you can show that \alpha a+b\in W then W is a subspace of \mathbb{R}^3.
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