## Quiz 13 (Part 1) Diagonalize a Matrix

## Problem 385

Let

\[A=\begin{bmatrix}

2 & -1 & -1 \\

-1 &2 &-1 \\

-1 & -1 & 2

\end{bmatrix}.\]
Determine whether the matrix $A$ is diagonalizable. If it is diagonalizable, then diagonalize $A$.

That is, find a nonsingular matrix $S$ and a diagonal matrix $D$ such that $S^{-1}AS=D$.