Problem

$$T=\begin{pmatrix} 2&3&7\\ 3&2&6\\ a&4&b \end{pmatrix} \qquad U=\begin{pmatrix} 6&-1&-4\\ 15&c&-9\\ -8&a&5 \end{pmatrix}$$

where $a$, $b$ and $c$ are constants.

Given that $TU=I$

(a) determine the value of $a$, the value of $b$ and the value of $c$

The transformation represented by the matrix $T$ transforms the line $l_1$ to the line $l_2$

Given that $l_2$ has equation

$$\frac{x-1}{3}=\frac{y}{-4}=z+2$$

(b) determine a Cartesian equation for $l_1$