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In a solution guide I've read that $\begin{bmatrix}a\\b\\c \end{bmatrix} : a+b+c=2$ isn't a vector space because it doesn't have the zero vector. I'm not 100% sure why this is but I think it's because if you make $a, b, c=0$ you don't get $2$ which is what it's meant to be equal to? Is my thinking correct or not?

Thanks

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    Yes, the coordinate sum of the zero vector is not $2$, hence $0\not\in V$. – 2017-02-16
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    Yea, no 0 vector implies no neutral element so the vector space isn't a group with respect to edition – 2017-02-16
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    Correct. Out if interest it isn't closed with respect to addition either (and probably doesn't satisfy other axioms too!). – 2017-02-16
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    "Yea, no 0 vector implies no neutral element so the vector space isn't a group with respect to edition". I wouldn't use the term "vector space" here! – 2017-02-16

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