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Reflection matrix

  • Thread starter Lchan1
  • Start date
  • #1
39
0

Homework Statement


Given the matrix A=
-1/2 root(3)/2
root(3)/2 1/2

determine if the matrix is a rotation about the origin or a reflection about the positive x axis
and find the angle between the that the line makes with the x-axis



Homework Equations





The Attempt at a Solution



I found the det(A)=-1 can I concluded that the matrix reflects vectors?
and also how do you find the angle?
I tried doing projection onto the axis. but didnt get me anywhere
please help..
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
249
Hi Lchan1! :smile:

(have a square-root: √ :wink:)
I found the det(A)=-1 can I concluded that the matrix reflects vectors?
Yup! :smile:
and also how do you find the angle?
learn this:

rotation through angle θ is

cosθ sinθ
-sinθ cosθ :wink:
 
  • #3
39
0
does that mean it's a rotation and a reflection?
pi/3 will be the angle?
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
249
does that mean it's a rotation and a reflection?
pi/3 will be the angle?
sorry, I was a bit too cryptic last time :redface:

a combination of a rotation and a reflection is a reflection …

it would have been better if I'd said

rotation through angle θ is

cosθ sinθ
-sinθ cosθ

reflection about y-axis is

-1 0
0 1

and if you combine them you get … ? :smile:
 

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