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Write the standard matrix for the composition of transformation for a vertical shear of mapping \( ...
Write the standard matrix for the composition of transformation for a vertical shear of mapping \( e_{1} \) to \( \left[\begin{array}{c}1 \\ -2\end{array}\right] \) but leaves \( e_{2} \) unchanged, followed by a rotation of \( 45^{\circ} \) counterclockwise.