Determine if the subset of ${\mathbb R}^{4}$ consisting of vectors of the form $\left[ \begin{array}{c} a \cr 2 a+b \cr 1 a - 3 b \cr 3 a+5 b \end{array} \right]$ is a subspace.

Select true or false for each statement.

True False  1. This set is a subspace

True False  2. This set is closed under scalar multiplications

True False  3. This set is closed under vector addition

True False  4. The set contains the zero vector