1. Euler-Rodrigues in matrix form. You have hopefully learnt that matrices can be interpreted as "concrete" representations of how vectors are transformed. Rotation in space is simply one special example of transforming (position) vectors. In this problem, we consider how a concrete rotation can be represented by exponentiating a suitable "generating" matrix. (a) As a warm up, let us consider a two-dimensional space. You might recall the rotation formula for coordinates in 2D: x = cos x sin y; y = sin x + cos y, (1) where we used an anti-clockwise = right-handed convention. This can be reasoned using the parametrization shown in Fig. 1 and its caption, and then apply the trigonometric sum- and-difference identities. Using a matrix and column-vector convention, we can repackage Eq. (1) into the following form