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Suppose that:

$$S=\bigg \{\left [\matrix { x \cr y}\right ] \bigg | \hskip .01in x+y\ge 0\bigg \}$$

Which of the following statements are true?

Select ALL that apply.

$S$ is a subspace of $R^2$.

$S$ is not closed under vector addition. For this reason, $S$ is not a subspace of $R^2$.

$S $ cannot be a subspace of $R^2$ since $S$ is not closed under multiplication by a scalar.

If $\vec v\in S$ and $\vec w\in S$, then $\vec v+\vec w\in S$.