Show that M indeed is a reflection. To do this, you need to find a (nonzero) column vector v such that Mv = v, another (nonzero) column vector w such that Mw=-w, and you need v and w to be perpendicular to each other. (This shows that M gives reflection across the line spanned by v, or in other words, Rv is the line of symmetry. Your job is to find v and w.
Show that M indeed is a reflection. To do this, you need to find a (nonzero) column vector v such that Mv = v, another (nonzero) column vector w such that Mw=-w, and you need v and w to be perpendicular to each other. (This shows that M gives reflection across the line spanned by v, or in other words, Rv is the line of symmetry. Your job is to find v and w.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
I need help with the second bullet point in d
Transcribed Image Text:cos
and
sin 0
simple and memorable form for the inverse.)
sin 0
une nonzero),
(6
(All but the first of these is a "special kind of matrix" and there is a
090).
(d) Consider the matrix M
-
Cos 0
sin 0
0
(13) (3) (
cos
sin 0
It is a fact that this gives counter-
cos (
(c) Consider the matrix M =
clockwise rotation around the origin by angle 0. On the basis of this fact, thinking geomet-
rically, what should the inverse matrix be? Explain how this agrees with your calculation in
(b) (using elementary trigonometry).
- sin
sin 0
- cos 0
utrices:
cos 0
sin 0
(e)
Going back to (b):
-
• (i 3¹); is a rotation. What is the angle? Sino
1
1
2
3 4
- sin 0
Cos 0
It is a fact that this is reflection
Sing-Co
across a a line.
. What should the inverse of a reflection be? Explain how this agrees with your answer
in (b).
Show that M indeed is a reflection. To do this, you need to find a (nonzero) column
vector v such that My = v, another (nonzero) column vector w such that Mw = -w, and
you need v and w to be perpendicular to each other. (This shows that M gives reflection
across the line spanned by v, or in other words, Rv is the line of symmetry. Your job is to
find v and w.
Expert Solution
Step 1
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
