Problem

$$M=\begin{pmatrix} 2&0&0\\ 0&1&4\\ 3&-2&-3 \end{pmatrix}$$

(a) Determine $M^{-1}$

The transformation represented by $M$ 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 $\Pi_2$

(b) Determine $x$, $y$ and $z$ in terms of $u$, $v$ and $w$ as appropriate.

The plane $\Pi_1$ has equation

$$3x-7y+2z=-3$$

(c) Find a Cartesian equation for $\Pi_2$

Give your answer in the form $au+bv+cw=d$ where $a$, $b$, $c$ and $d$ are integers to be determined.