Diagonalization and matrix powers
Let
- Determine whether
is diagonalizable, and if so, give its diagonal form along with a diagonalizing matrix. - Compute
. Remember to show all work.
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Let $A=\begin{bmatrix} 0 & 0 & -2 \\ 1 & 2 & 1 \\ 1 & 0 & 3\end{bmatrix}$.
\begin{enumerate}[label=\alph*)]
\item Determine whether $A$ is diagonalizable, and if so, give its diagonal form along with a diagonalizing matrix.
\item Compute $A^{42}$. Remember to show all work.
\end{enumerate}