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Math Help - Subspaces.

  1. #1
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    Subspaces.

    6. Let W= (a): a + b + c = 0). Is W a subspace of R^3
    (b)
    (c)
    Last edited by mr fantastic; March 1st 2011 at 05:33 PM. Reason: Re-titled.
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  2. #2
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    the question must be,
    W=\left \{ (a,b,c)\in \mathbb{R}^{3}\mid a+b+c=0  \right \} is it a subspace of \mathbb{R}^{3} ?
    Now can you answer these questions ?
    is it closed under addition ?
    is it closed under scalar multiplication ?
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  3. #3
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    abc is not horizontal, it's vertical if it changes anything. And to be honest I have no idea how to do this problem. My teacher had this problem on the homework and we literally did not learn anything yet. I would ask for the answer but it's not fair to ask that on here.
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  4. #4
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    Let X=(a,b,c) and X'=(a',b',c') elements of W.We have also X+X'= (a+a',b+b',c+c') element of W.Indeed,
    (a+a')+(b+b')+(c+c')=(a+b+c)+(a'+b'+c')=0
    This proves that W is closed under addition,try to prove that is also closed under scalar multiplication.
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