- In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
$$\mathbf { M } = \left( \begin{array} { r r r }
2 & 0 & 0
0 & 1 & 4
3 & - 2 & - 3
\end{array} \right)$$
- Determine \(\mathbf { M } ^ { - 1 }\)
The transformation represented by \(\mathbf { M }\) maps the plane \(\Pi _ { 1 }\) to the plane \(\Pi _ { 2 }\) The point \(( x , y , z )\) on \(\Pi _ { 1 }\) maps to the point \(( u , v , w )\) on \(\Pi _ { 2 }\)
- Determine \(x , y\) and \(z\) in terms of \(u , v\) and \(w\) as appropriate.
The plane \(\Pi _ { 1 }\) has equation
$$3 x - 7 y + 2 z = - 3$$
- Find a Cartesian equation for \(\Pi _ { 2 }\)
Give your answer in the form \(a u + b v + c w = d\) where \(a , b , c\) and \(d\) are integers to be determined.