$$\[ \mathbf{M}=\left(\begin{array}{rrr} 2 & 0 & 3 \\ 0 & -4 & -3 \\ 0 & -4 & 0 \end{array}\right) \]$$ Given that $$\(\mathbf{M}\)$$ has exactly two distinct eigenvalues $$\(\lambda_{1}\)$$ and $$\(\lambda_{2}\)$$ where $$\(\lambda_{1}< \lambda_{2}\)$$ The line $$\(l_{1}\)$$ has equation $$\(\mathbf{r}=\left(\begin{array}{r}4 \\ -1 \\ 0\end{array}\right)+\mu\left(\begin{array}{r}2 \\ 0 \\ -1\end{array}\right)\)$$, where $$\(\mu\)$$ is a scalar parameter. The transformation $$\(T\)$$ is represented by $$\(\mathbf{M}\)$$. The line $$\(l_{1}\)$$ is transformed by $$\(T\)$$ to the line $$\(l_{2}\)$$ (b) Determine a vector equation for $$\(l_{2}\)$$, giving your answer in the form $$\(\mathbf{r} \times \mathbf{b}=\mathbf{c}\)$$ where $$\(\mathbf{b}\)$$ and $$\(\mathbf{c}\)$$ are constant vectors. (3)

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