題組內容

3. Given a matrix \( A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 0 \end{bmatrix} \) and evaluate the following:

(c) Find an orthogonal matrix $P$, that is $P^{-1}=P^T$, such that $P^{-1}AP=D$, where D is the diagonal matrix of the eigenvalues of A. (10%)