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\\
(i) the rank of $\mathbf { M }$ and a basis for the range space of T ,\\
(ii) a basis for the null space of T .

\hfill \mbox{\textit{CAIE FP1 2011 Q4}}