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Question 3.30: (a) Find the reflection of R3 along the direction v3= (−1, 1...

(a) Find the reflection of R³ along the direction \overrightarrow{v_{3}} =\left(-1,1,-1\right) with respect to the plane \left(2,-2,3\right)+\ll \left(0,1,0\right),\left(0,-1,1\right)\gg.

(b) Show that

T\left(\overrightarrow{x}\right)=\overrightarrow{x_{0}}+\overrightarrow{x}A,  where  \overrightarrow{x_{0}}=\left(0,-2,-4\right)  and  A = \left[\begin{matrix} 1 & 0 & 0 \\ \\  0 & \frac{5}{3} & \frac{4}{3} \\ \\  0 & -\frac{4}{3} & -\frac{5}{3} \end{matrix} \right]

is a reflection. Determine its direction and plane of invariant points.

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