Determine if the subset of ${\mathbb R}^{3}$ consisting of vectors of the form $\left[ \begin{array}{c} a \cr b \cr c \end{array} \right]$, where at most one of $a$, $b$, and $c$ is nonzero, is a subspace.

Select true or false for each statement.

True False  1. The set contains the zero vector

True False  2. This set is closed under vector addition

True False  3. This set is closed under scalar multiplications

True False  4. This set is a subspace