6. The matrix \(\mathbf { M }\) is given by
$$\mathbf { M } = \left[ \begin{array} { l l l }
2 & 1 & 3
1 & 3 & 2
3 & 2 & 5
\end{array} \right]$$
- Find
- the adjugate matrix of \(\mathbf { M }\),
- hence determine the inverse matrix \(\mathbf { M } ^ { - 1 }\).
- Use your result to solve the simultaneous equations
$$\begin{aligned}
& 2 x + y + 3 z = 13
& x + 3 y + 2 z = 13
& 3 x + 2 y + 5 z = 22
\end{aligned}$$