14 The matrix \(\mathbf { M }\) is defined as
$$\mathbf { M } = \left[ \begin{array} { c c c }
5 & 2 & 1
6 & 3 & 2 k + 3
2 & 1 & 5
\end{array} \right]$$
where \(k\) is a constant.
14
- Given that \(\mathbf { M }\) is a non-singular matrix, find \(\mathbf { M } ^ { - 1 }\) in terms of \(k\)
14 - State any restrictions on the value of \(k\)
14
- Using your answer to part (a), show that the solution to the set of simultaneous equations below is independent of the value of \(k\)
$$\begin{array} { r l c c }
5 x + 2 y + c & = & 1
6 x + 3 y + ( 2 k + 3 ) z & = & 4 k + 3
2 x + y + 5 z & = & 9
\end{array}$$