Elementary mappings/Linear/Diagonalizable/Trigonalizable/1/Exercise

Determine, which of the following elementary-geometric mappings are linear, which are diagonalizable and which are trigonalizable.

1. The reflection in the plane, given by the line ${}4x-7y=0$ as axis.
2. The translation with the vector ${}\left(5,\,-3\right)$.
3. The rotation by ${}30$ degree counter-clockwise around the origin.
4. The reflection with ${}(1,0)$ as center.

Create a solution