2. The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { c c c } \lambda & 1 & 14
- 1 & 2 & 8
- 3 & 2 & \lambda \end{array} \right)\), where \(\lambda\) is a real constant.
- Find an expression for the determinant of \(\mathbf { A }\) in terms of \(\lambda\). Give your answer in the form \(a \lambda ^ { 2 } + b \lambda + c\), where \(a , b , c\) are integers whose values are to be determined.
- Show that \(\mathbf { A }\) is non-singular for all values of \(\lambda\).