5 The linear transformation \(\mathrm { T } : \mathbb { R } ^ { 4 } \rightarrow \mathbb { R } ^ { 4 }\) is represented by the matrix \(\mathbf { M }\), where
$$\mathbf { M } = \left( \begin{array} { r r r r }
1 & 2 & 0 & 4
5 & 2 & 1 & - 3
4 & 0 & 1 & - 7
- 2 & 4 & - 1 & \alpha
\end{array} \right)$$
It is given that the rank of \(\mathbf { M }\) is 2 .
- Find the value of \(\alpha\) and state a basis for the range space of T .
- Obtain a basis for the null space of T .