題組內容

二、所有題目請敘述計算過程，無計算過程不給分
(1). Let A = $\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$

(c) Orthogonally diagonalize the matrix A. (You need to find out an orthogonal matrix P and a diagonal matrix D such that $ \mathrm{P}^{\mathrm{T}}\mathrm{A}\mathrm{P} = \mathrm{D} $.) (10%)