- Matrix \(\mathbf { M }\) is given by
$$\mathbf { M } = \left( \begin{array} { r r r }
1 & 0 & a
- 3 & b & 1
0 & 1 & a
\end{array} \right)$$
where \(a\) and \(b\) are integers, such that \(a < b\)
Given that the characteristic equation for \(\mathbf { M }\) is
$$\lambda ^ { 3 } - 7 \lambda ^ { 2 } + 13 \lambda + c = 0$$
where \(c\) is a constant,
- determine the values of \(a , b\) and \(c\).
- Hence, using the Cayley-Hamilton theorem, determine the matrix \(\mathbf { M } ^ { - 1 }\)