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

$$\mathbf { M } = \left( \begin{array} { r r r r } 
2 & - 1 & 1 & 3 \\
2 & 0 & 0 & 5 \\
6 & - 2 & 2 & 11 \\
10 & - 3 & 3 & 19
\end{array} \right)$$

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

\hfill \mbox{\textit{CAIE FP1 2014 Q6}}