6.
$$\mathbf { M } = \left( \begin{array} { r r r }
k & 5 & 7
1 & 1 & 1
2 & 1 & - 1
\end{array} \right) \quad \text { where } k \text { is a constant }$$
- Given that \(k \neq 4\), find, in terms of \(k\), the inverse of the matrix \(\mathbf { M }\).
- Find, in terms of \(p\), the coordinates of the point where the following planes intersect.
$$\begin{array} { r }
2 x + 5 y + 7 z = 1
x + y + z = p
2 x + y - z = 2
\end{array}$$ - Find the value of \(q\) for which the following planes intersect in a straight line.
$$\begin{array} { r }
4 x + 5 y + 7 z = 1
x + y + z = q
2 x + y - z = 2
\end{array}$$ - For this value of \(q\), determine a vector equation for the line of intersection.