(a) Diagonalize the matrix $\left[\begin{array}{ccc}2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2\end{array}\right]$.
Explanation
Diagonalization of a matrix involves finding its eigenvalues and eigenvectors, and then forming a new matrix whose columns are the eigenvectors and a diagonal matrix whose diagonal entries are the eigenvalues.
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