\(\begin{pmatrix}t-4 & 0 & 0\\ -1 & t+1 & 1\\3 & 4 & t-2\end{pmatrix}\) = 0 t - 4\(\begin{pmatrix}t+1 & 1\\4 & t-2\end{pmatrix}\) + 0\(\begin{pmatrix}-1 & 1\\3 & t-2\end{pmatrix}\) + 0\(\begin{pmatrix}-1 & t+1\\3 & 4\end{pmatrix}\) t - 4[(t + 1)(t - 1) - 4] = 0 (t - 4)[ t\(^2\) - t - 6] = 0 = (t - 4)((t - 3)(t + 2) = 0 t = 4 or -2 or 3