Matrix description of transformations in a plane

Extract

Any simple transformation that leaves the origin unchanged corresponds to multiplication by a 2 × 2 matrix which can generally be written down at sight. Transformations such as translations, under which the origin moves, cannot be represented in this simple manner. However, by moving into three dimensions this deficiency can be made good. Furthermore, the exercise gives useful experience of thinking in three dimensions and a useful addition to the repertoire of matrices.