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Thread: Proving (or not) if a subset of R^3 is a subspace part 2,3, and 4

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    Proving (or not) if a subset of R^3 is a subspace part 2,3, and 4

    I already posted one of these proofs, but I figured I would combine the rest into an album and submit them at once.

    The questions is to prove if the given subsets are a subspace of R^3.

    I'm confident that I did a and b well enough. For c, I did not know how to handle the inequality, so I did what I thought was best. I am also worried because it says to prove or disprove, and all mine are proofs..

    I would appreciate any feed back on my proofs.

    https://imgur.com/a/LYHEptt
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    Re: Proving (or not) if a subset of R^3 is a subspace part 2,3, and 4

    Quote Originally Posted by MrJank View Post
    For c, I did not know how to handle the inequality, so I did what I thought was best. I am also worried because it says to prove or disprove, and all mine are proofs..
    For 1c)
    $\vec a = {\left\langle {1,2,3} \right\rangle ^T}~\&~\vec b = {\left\langle { - 2,4,3} \right\rangle ^T}\text{ then }~\vec a + ( - 1)\vec b = ?$
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    Re: Proving (or not) if a subset of R^3 is a subspace part 2,3, and 4

    Quote Originally Posted by Plato View Post
    For 1c)
    $\vec a = {\left\langle {1,2,3} \right\rangle ^T}~\&~\vec b = {\left\langle { - 2,4,3} \right\rangle ^T}\text{ then }~\vec a + ( - 1)\vec b = ?$
    a would be greater than c, violating the rules of the subspace? That would mean it is not closed under addition?
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