Let Y , P, and R be the yaw, pitch, and roll matrices given in equations (1), (2), and (3), and let Q = Y PR.
(a) Show that Y , P, and R all have determinants equal to 1.
(b) The matrix Y represents a yaw with angle u. The inverse transformation should be a yaw with angle −u. Show that the matrix representation of the inverse transformation is Y T and that Y T = Y −1.
(c) Show that Q is nonsingular, and express Q−1 in terms of the transposes of Y , P, and R.
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