4 The linear transformation \(\mathrm { T } : \mathbb { R } ^ { 4 } \rightarrow \mathbb { R } ^ { 4 }\) is represented by the matrix \(\mathbf { M }\), where
$$\mathbf { M } = \left( \begin{array} { r r r r }
3 & 4 & 2 & 5
6 & 7 & 5 & 8
9 & 9 & 9 & 9
15 & 16 & 14 & 17
\end{array} \right)$$
Find
- the rank of \(\mathbf { M }\) and a basis for the range space of T ,
- a basis for the null space of T .