If $T:{\mathbb R}^5\to {\mathbb R}^2$ is a linear transformation, then select true or false for each statement about the set $\ker( T)$.

True False  1. This set contains the zero vector and is closed under vector addition and scalar multiplication.

True False  2. This set is a subset of the codomain.

True False  3. This set is a subspace of $\mathbb{R}^2$.

True False  4. This set is a subset of the domain.