# Question 3.35: Give an affine transformation T(x^→ ) = x0^→ + x^→ A, where ...

Give an affine transformation

T\left(\overrightarrow{x}\right)=\overrightarrow{x_{0} }+\overrightarrow{x}A, where A =\left[\begin{matrix} \frac{1}{3} & \frac{2}{3} & \frac{2}{3} \\ \\ \frac{2}{3} & \frac{1}{3} & -\frac{2}{3} \\ \\ \frac{2}{3} & -\frac{2}{3} & \frac{1}{3} \end{matrix} \right] .

Determine these \overrightarrow{x_{0} } so that each such T is an orthogonal reflection, and the direction and the plane of invariant points.

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