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%)