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Is this a subspace $S=\left\{A\in M_3:\:\begin{pmatrix}1\\ 1\\ 1\end{pmatrix}\in R\left(A\right)\right\}$ of $M_{3x3}(\mathbb{R})$

The usual way to check is to choose two vectors from the subspace and check if their addition gives back a vector from the same subspace, but what do vectors from this space look like? The condition states that such a vector must have (1,1,1) in it's column space, how to choose such vectors?

P.S. Also in my opinion it's not a subspace because choosing the zero matrix we find out that it is not in $S$.

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    What does $R\left(A\right)$ mean precisely? – 2017-02-06
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    Isn't $R(A)$ usually denoted the **row space** and not the **column space**? – 2017-02-06
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    Mr @Travis it's not so it should not be a subspace? – 2017-02-06
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    Correct, as you indicate, every vector subspace must include the zero element. – 2017-02-06

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