Find the basis and dimension of vector space over $\mathbb R$:

a) vector space generated by $\{u+v+w,v+w+z,w+z+u,z+u+v\}$, where $u,v,w,z$ are linearly independent vectors of some vector space

b) $R(A) \cap S(A) \cap Ker(A)$ for matrix $$
 A= \begin{pmatrix}
 1 & 2 \\
 3 & 5 \\
 \end{pmatrix}$$

$R(A)$ is row matrix space, $S(A)$ is column matrix space and $Ker(A)$ is kernel of the matrix.

How to reduce this vector in a) to get the basis? I'm not sure how to calculate $R(A) \cap S(A) \cap Ker(A)$. Will $R(A)$ and $S(A)$ be the same for matrix 2x2? Could someone help me please?