\(Q = \begin{bmatrix} 1 & 0 & 0 \\ \answer {0} & 1/\sqrt {2} & 1/\sqrt {2} \\ \answer {0} & 1/\sqrt {2} & \answer {-1/\sqrt {2}} \end{bmatrix}\)
If \(A = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 3 & 7 \\ 0 & 7 & 3 \end{bmatrix}\), find an orthogonal matrix \(Q\) such that \(Q^{-1}AQ\) is diagonal.