Expert Answer to "Determine the matrix representation of each of the..."

High School
Geometry
High school geometry
Performing transformations

glasskerfu

Answered question

2020-11-30

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

Answer & Explanation

Theodore Schwartz

Skilled2020-12-01Added 99 answers

If L is pitch transformation with the angle of theta, the matrix representation of L is given by,
$p = [(\cos θ, \sin θ, o), (- \sin θ, \cos θ, 0), (0, 0, 1)]$
If L is the pitch transformation with the angle of rotation phi, the matrix representation of L is given by
$[(\cos ϕ, 0, - \sin ϕ), (0, 1, 0), (\sin ϕ, 0, \cos ϕ)]$
$p y = [((\cos 90^{\circ}), (\sin 90^{\circ}), 0), ((- \sin 90^{\circ}), (\cos 90^{\circ}), 0), (0, 0, 1)] [((\cos 90^{\circ}), 0, (- \sin 90^{\circ})), (0, 1, 0), ((\sin 90 v), 0, (\cos 90^{\circ}))]$
$= [(0, 1, 0), (- 1, 0, 0), (0, 0, 1)] [(0, 0, - 1), (0, 1, 0), (1, 0, 0)]$
$= [(0, 1, 0), (0, 0, 1), (1, 0, 0)]$

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