- In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
$$\mathbf { A } = \left( \begin{array} { r r }
3 & k
- 5 & 2
\end{array} \right)$$
where \(k\) is a constant.
Given that there exists a matrix \(\mathbf { P }\) such that \(\mathbf { P } ^ { - 1 } \mathbf { A P }\) is a diagonal matrix where
$$\mathbf { P } ^ { - 1 } \mathbf { A } \mathbf { P } = \left( \begin{array} { r r }
8 & 0
0 & - 3
\end{array} \right)$$
- show that \(k = - 6\)
- determine a suitable matrix \(\mathbf { P }\)