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Question 3.34: Give an affine transformation T(x^→ ) = x0^→ + x^→A, where A...

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{2}{3} & \frac{1}{3} \\ \\  \frac{2}{3} & -\frac{1}{3} & -\frac{2}{3} \end{matrix} \right] .

Try to determine these \overrightarrow{x_{0}} so that T is a rotation. In this case, determine the axis and the angle of the rotation, also the rotational plane.

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