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a) Find the 3 x 3 matrix Y that describes a rotation by 30° about the y-axis in 3-dimensional space. b) Find the 3 x 3 matrix X that describes a rotation by 45° about the z-axis in 3-dimensional space. c) Compute the products YX and XY. Draw sequences of pictures of cubes to visualize both rotations (imitate what we did for 90° rotations in the lecture: draw the cube in original position, then after having applied the first rotation, and in final position after the second rotation.)

a) Find the 3 x 3 matrix Y that describes a rotation by 30° about the y-axis in 3-dimensional space. b) Find the 3 x 3 matrix X that describes a rotation by 45° about the z-axis in 3-dimensional space. c) Compute the products YX and XY. Draw sequences of pictures of cubes to visualize both rotations (imitate what we did for 90° rotations in the lecture: draw the cube in original position, then after having applied the first rotation, and in final position after the second rotation.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Task 6 a) Find the 3 x 3 matrix Y that describes a rotation by 30° about the y-axis in 3-dimensional space. b) Find the 3 x 3 matrix X that describes a rotation by 45° about the z-axis in 3-dimensional space. c) Compute the products YX and XY. Draw sequences of pictures of cubes to visualize both rotations (imitate what we did for 90° rotations in the lecture: draw the cube in original position, then after having applied the first rotation, and in final position after the second rotation.)
Transcribed Image Text:Task 6 a) Find the 3 x 3 matrix Y that describes a rotation by 30° about the y-axis in 3-dimensional space. b) Find the 3 x 3 matrix X that describes a rotation by 45° about the z-axis in 3-dimensional space. c) Compute the products YX and XY. Draw sequences of pictures of cubes to visualize both rotations (imitate what we did for 90° rotations in the lecture: draw the cube in original position, then after having applied the first rotation, and in final position after the second rotation.)
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