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(a) Determine the transformation matrix describing a reflection at the axis y = -x+3 in homogenous coordinates. (b) Given are the three points \mathbf{x}_{1}=\left(\begin{array}{l}

0 \\

1

\end{array}\right), \mathbf{x}_{2}=\left(\begin{array}{l}

1 \\

0

\end{array}\right), \mathbf{x}_{3}=\left(\begin{array}{l}

1 \\

2

\end{array}\right) as well as their images after transformation \mathbf{x}_{1}^{\prime}=\left(\begin{array}{c}

-1 \\

5

\end{array}\right), \mathbf{x}_{2}^{\prime}=\left(\begin{array}{c}

-1 \\

1

\end{array}\right), \mathbf{x}_{3}^{\prime}=\left(\begin{array}{l}

1 \\

5

\end{array}\right) Determine the affine transformation matrix T in homogenous coordinates such that x = Tx; for i = 1,2,3! (c) Determine the transformation matrix T in homogenous coordinates for the following transformation: \left(\begin{array}{l}

x \\

y

\end{array}\right) \longmapsto\left(\begin{array}{c}

\cos ^{2} \alpha x-\sin ^{2} \alpha y+\frac{\pi}{2} \\

\tan ^{2} \alpha y+\cos ^{2} \alpha x-\pi

\end{array}\right) (d) Determine the transformation matrix T in homogenous coordinates for the following transformation: \left(\begin{array}{l}

x \\

y

\end{array}\right) \longmapsto\left(\begin{array}{c}

\pi \\

\frac{3 y}{x+\pi}+2

\end{array}\right)

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