$$\[ \mathbf{T}=\left(\begin{array}{lll} 2 & 3 & 7 \\ 3 & 2 & 6 \\ a & 4 & b \end{array}\right) \quad \mathbf{U}=\left(\begin{array}{rrr} 6 & -1 & -4 \\ 15 & c & -9 \\ -8 & a & 5 \end{array}\right) \]$$ where $$\(a, b\)$$ and $$\(c\)$$ are constants. Given that $$\(\mathbf{T U}=\mathbf{I}\)$$ The transformation represented by the matrix $$\(\mathbf{T}\)$$ transforms the line $$\(l_{1}\)$$ to the line $$\(l_{2}\)$$ Given that $$\(l_{2}\)$$ has equation $$\[ \frac{x-1}{3}=\frac{y}{-4}=z+2 \]$$ (b) determine a Cartesian equation for $$\(l_{1}\)$$ (4)

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