(Solved): Consider a \( 2 \times 2 \) matrix \( A=\left[\begin{array}{ll}2 & 0 \\ 0 & 1 ...

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Consider a \( 2 \times 2 \) matrix \( A=\left[\begin{array}{ll}2 & 0 \\ 0 & 1\end{array}\right] \). Find an orthogonal matrix \( 2 \times 2 \)-matrix \( Q \) and a diagonal \( 2 \times 2 \) matrix \( D \) such that \( A=Q D Q^{T} \). Note: In order to be accepted as correct, all entries of the matrices \( A-Q D Q^{T} \) and \( Q^{T} Q-I \) must have absolute value smaller than \( 0.05 \). Additional attempts available with new variants