Determine the matrix representation of each of the following composite transformations. (a) A yaw of 90 ° , followed by a pitch of 90 ° . (b) A pitch of 90 ° , followed by a yaw of 90 ° . (c) A pitch of 45 ° , followed by a roll of − 90 ° . (d) A roll of − 90 ° , followed by a pitch of 45 ° . (e) A yaw of 45 ° , followed by a pitch of − 90 ° and then a roll of − 45 ° . (f) A roll of − 45 ° , followed by a pitch of − 90 ° and then a yaw of 45 °
Determine the matrix representation of each of the following composite transformations. (a) A yaw of 90 ° , followed by a pitch of 90 ° . (b) A pitch of 90 ° , followed by a yaw of 90 ° . (c) A pitch of 45 ° , followed by a roll of − 90 ° . (d) A roll of − 90 ° , followed by a pitch of 45 ° . (e) A yaw of 45 ° , followed by a pitch of − 90 ° and then a roll of − 45 ° . (f) A roll of − 45 ° , followed by a pitch of − 90 ° and then a yaw of 45 °
Determine the matrix representation of each of the following composite transformations. (a) A yaw of
90
°
, followed by a pitch of
90
°
. (b) A pitch of
90
°
, followed by a yaw of
90
°
. (c) A pitch of
45
°
, followed by a roll of
−
90
°
. (d) A roll of
−
90
°
, followed by a pitch of
45
°
. (e) A yaw of
45
°
, followed by a pitch of
−
90
°
and then a roll of
−
45
°
. (f) A roll of
−
45
°
, followed by a pitch of
−
90
°
and then a yaw of
45
°
Suppose that vertices of a hut-shaped triangle on a computer screen are given by the coordinates (1, 0), (5,
0). (5, 3). (3, 5) & (1, 3). Transform this hut in following order
1. Reflect it along x-axis
2. Rotate it 180° counterclockwise
i.
Write 2*2 matrices for each transformation. Representing the above hut-shaped in form of data
matrix, apply these transformations one by one and draw it at each step
Find a single matrix of the composite transformation which performs both transformations at
once. Apply it to the hut and draw it. It should be the same with the one obtained in part i.
ii.
Find the value of h,k, and a. And describe the transformation
Chapter 4 Solutions
Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))
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