Question

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

Answer 1

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
\([(\cos\phi, 0, -\sin\phi),(0,1,0),(\sin\phi,0,\cos\phi)]\)
\(py=[((\cos90^{\circ}),(\sin90^{\circ}), 0),((-\sin90^{\circ}) , (\cos90^{\circ}),0),(0,0,1)] [((\cos90^{\circ}),0,(-\sin90^{\circ})),(0,1,0),((\sin90v),0, (\cos90^{\circ}))]\)
\(=[(0, 1, 0),(-1, 0, 0),(0, 0, 1)][(0, 0, -1),(0, 1, 0),(1, 0, 0)]\)
\(=[(0, 1, 0),(0, 0, 1),(1, 0, 0)]\)