5 The linear transformation \(\mathrm { T } : \mathbb { R } ^ { 4 } \rightarrow \mathbb { R } ^ { 4 }\) is represented by the matrix \(\mathbf { M }\), where
$$\mathbf { M } = \left( \begin{array} { r r r r }
3 & 2 & 0 & 1
6 & 5 & - 1 & 3
9 & 8 & - 2 & 5
- 3 & - 2 & 0 & - 1
\end{array} \right)$$
- Find the rank of \(\mathbf { M }\).
Let \(K\) be the null space of T . - Find a basis for \(K\).
- Find the general solution of
$$\mathbf { M } \mathbf { x } = \left( \begin{array} { r }
2
5
8
- 2
\end{array} \right) .$$