Question

# Determine the matrix representation of each of the following composite transformations. A pitch of 90^(circ) followed by a yaw of 90^(circ)

Performing transformations

Determine the matrix representation of each of the following composite transformations. A pitch of $$90^{\circ}$$ followed by a yaw of $$90^{\circ}$$

2020-12-01

If L is pitch transformation with the angle of theta, the matrix representation of L is given by,
$$p=[(\cos\theta, \sin\theta, o),(-\sin\theta, \cos\theta, 0),(0,0,1)]$$
If L is the pitch transformation with the angle of rotation phi, the matrix representation of L is given by
$$[(\cos\phi, 0, -\sin\phi),(0,1,0),(\sin\phi,0,\cos\phi)]$$
$$py=[((\cos90^{\circ}),(\sin90^{\circ}), 0),((-\sin90^{\circ}) , (\cos90^{\circ}),0),(0,0,1)] [((\cos90^{\circ}),0,(-\sin90^{\circ})),(0,1,0),((\sin90v),0, (\cos90^{\circ}))]$$
$$=[(0, 1, 0),(-1, 0, 0),(0, 0, 1)][(0, 0, -1),(0, 1, 0),(1, 0, 0)]$$
$$=[(0, 1, 0),(0, 0, 1),(1, 0, 0)]$$