4.
$$\mathbf { M } = \left( \begin{array} { r r r }
2 & 1 & 4
k & 2 & - 2
4 & 1 & - 2
\end{array} \right) \quad \mathbf { N } = \left( \begin{array} { r r r }
k - 7 & 6 & - 10
2 & - 20 & 24
- 3 & 2 & - 1
\end{array} \right)$$
where \(k\) is a constant.
- Determine, in simplest form in terms of \(k\), the matrix \(\mathbf { M N }\).
- Given that \(k = 5\)
- write down \(\mathbf { M N }\)
- hence write down \(\mathbf { M } ^ { - 1 }\)
- Solve the simultaneous equations
$$\begin{aligned}
& 2 x + y + 4 z = 2
& 5 x + 2 y - 2 z = 3
& 4 x + y - 2 z = - 1
\end{aligned}$$ - Interpret the answer to part (c) geometrically.