6 The linear transformation \(\mathrm { T } : \mathbb { R } ^ { 4 } \rightarrow \mathbb { R } ^ { 4 }\) is represented by the matrix \(\mathbf { M }\), where
$$\mathbf { M } = \left( \begin{array} { r r r r }
2 & - 1 & 1 & 3
2 & 0 & 0 & 5
6 & - 2 & 2 & 11
10 & - 3 & 3 & 19
\end{array} \right)$$
- Find the rank of \(\mathbf { M }\) and state a basis for the range space of T .
- Obtain a basis for the null space of T .