= Solution
On $\mathbb C^3$ take the <matrix units>
$$
\boxed{\rho(p)=E_{12},\qquad\rho(q)=E_{23},\qquad\rho(c)=E_{13}.}
$$
Their products give $[E_{12},E_{23}]=E_{13}$, while $E_{13}$ commutes with each of the other two. Thus this is a <Lie algebra representation>. The three images are <linearly independent>, so its <kernel> is zero: it is \b[faithful and finite-dimensional]. It is reducible, as expected from the classification in part ii; for example, the first coordinate line is invariant.
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