6 The linear transformation \(\mathrm { T } : \mathbb { R } ^ { 4 } \rightarrow \mathbb { R } ^ { 4 }\) is represented by the matrix \(\mathbf { M }\), where $$\mathbf { M } = \left( \begin{array} { r r r r } - 2 & 5 & 3 & - 1
0 & 1 & - 4 & - 2
6 & - 14 & - 13 & 1
\alpha & \alpha & - 2 \alpha & - 11 \alpha \end{array} \right)$$ and \(\alpha\) is a constant. The null space of T is denoted by \(K _ { 1 }\) when \(\alpha \neq 0\), and by \(K _ { 2 }\) when \(\alpha = 0\). Find a basis for \(K _ { 1 }\) and a basis for \(K _ { 2 }\).