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step-by-step
\begin{pmatrix} \frac{1}{\sqrt{6}} & \frac{1}{\sqrt{6}} & \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{2}} &-\frac{1}{\sqrt{2}} & 0 \\ -\frac{1}{\sqrt{3}} &-\frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}}\end{pmatrix}\begin{pmatrix} -2 & 1 & 2 \\ 1 &-2 & 2 \\ 2 & 2 & 1\end{pmatrix}\begin{pmatrix} \frac{1}{\sqrt{6}} & \frac{1}{\sqrt{6}} & \frac{2}{\sqrt{6}} \\ \frac{1}{\sqrt{2}} &-\frac{1}{\sqrt{2}} & 0 \\ -\frac{1}{\sqrt{3}} &-\frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}}\end{pmatrix}^{T}
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