5 The linear transformation $\mathrm { T } : \mathbb { R } ^ { 4 } \rightarrow \mathbb { R } ^ { 4 }$ is represented by the matrix $\mathbf { A }$, where

$$\mathbf { A } = \left( \begin{array} { r r r r } 
1 & 3 & 5 & 7 \\
2 & 8 & 7 & 9 \\
3 & 13 & 9 & 11 \\
6 & 24 & 21 & 27
\end{array} \right)$$

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

\hfill \mbox{\textit{CAIE FP1 2016 Q5}}