6. What 3 by 3 matrices represent the transformations that (a) project every vector onto the x-y plane? (b) reflect every vector through the x-y plane? (c) rotate the x-y plane through 90°, leaving the z-axis alone? (d) rotate the x-y plane, then x-z, then y-z, through 90°? (e) carry out the same three rotations, but each one through 180°?
6. What 3 by 3 matrices represent the transformations that (a) project every vector onto the x-y plane? (b) reflect every vector through the x-y plane? (c) rotate the x-y plane through 90°, leaving the z-axis alone? (d) rotate the x-y plane, then x-z, then y-z, through 90°? (e) carry out the same three rotations, but each one through 180°?
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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Question
Transcribed Image Text:6. What 3 by 3 matrices represent the transformations that
(a) project every vector onto the x-y plane?
(b) reflect every vector through the x-y plane?
(c) rotate the x-y plane through 90°, leaving the z-axis alone?
(d) rotate the x-y plane, then x-z, then y-z, through 90°?
(e) carry out the same three rotations, but each one through 180°?
Expert Solution
Step 1
To find : 3 by 3 matrices represent the transformation that
(a) project every vector onto the x-y plane.
(b) Reflect every vector through the r-y plane.
(c) Rotate the x-y plane through 90°, leaving the z-axis alone.
(d) Rotate the x-y plane, then x-z, then y-2, through 90°.
(e) Carry out the same three rotations, but each one through 180°.
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