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
- the rank of \(\mathbf { A }\),
- a basis for the range space of T ,
- a basis for the null space of T .