Find the inverse of the matrix \(\left( \begin{array} { r r r } 4 & 1 & k 3 & 2 & 5 8 & 5 & 13 \end{array} \right)\), where \(k \neq 5\).
Solve the simultaneous equations
$$\begin{aligned}
& 4 x + y + 7 z = 12
& 3 x + 2 y + 5 z = m
& 8 x + 5 y + 13 z = 0
\end{aligned}$$
giving \(x , y\) and \(z\) in terms of \(m\).
Find the value of \(p\) for which the simultaneous equations
$$\begin{aligned}
& 4 x + y + 5 z = 12
& 3 x + 2 y + 5 z = p
& 8 x + 5 y + 13 z = 0
\end{aligned}$$
have solutions, and find the general solution in this case.