Linear Algebra reflection question

  • Thread starter Perrry
  • Start date
  • #1
Perrry
Hi this is my first post here. So be nice now o:) I´ve have a problem with a question:

[tex]T:\mathbb{R}^2\rightarrow\mathbb{R}^2 [/tex] first reflects points through the vertical x2-axis and then rotates points [tex]\pi[/tex]/2 radians.


/Perrry
 

Answers and Replies

  • #2
998
69
What's the question?
 
  • #3
radou
Homework Helper
3,120
7
Perrry said:
Hi this is my first post here. So be nice now o:) I´ve have a problem with a question:

[tex]T:\mathbb{R}^2\rightarrow\mathbb{R}^2 [/tex] first reflects points through the vertical x2-axis and then rotates points [tex]\pi[/tex]/2 radians.


/Perrry

What does 'x2-axis' mean? You mean like the y-axis in an orthogonal x-y coordinate system? What is your direction of rotation? Do you have to write the operator T in matrix form? State your question more clear, please.
 
  • #4
Perrry
Okay sorry my english isn´t that good. I missed some trival parts....

T is a linear tranformation. And i shall find the standard matrix of T. The x2 axis is the Y-axis. And the rotation should be counterclockwise.

//Perrry
 
  • #5
radou
Homework Helper
3,120
7
To illustrate the problem, place a point T1 somewhere in the x-y coordinate system. Then follow the rules and get T1' and T1''. T1'' represents the point you get after the operator T is applied. So, write a matrix equation of form T1 T = T1'', whete T is your linear operator, which is a 2x2 matrix. Solve the equation, and you should get the elements of T.
 
  • #6
Perrry
Okay. The first matrix that reflects the points through the y-axis is [tex]
\left[
\begin{array}{cc}
-1 & 0\\
0 & 1
\end{array}
\right]
[/tex]

and then the matrix that rotate them counterclockwise is [tex] \left[ \begin{array}{cc}
0 & -1\\
1 & 0
\end{array}
\right]
[/tex]

I should write them in a matrix that first reflects the points through the x-axis and then rotate them pi/2. Could i just write:

[tex]T= \left[ \begin{array}{cc}
-1 & 0\\
0 & 1
\end{array}
\right]
[/tex] [tex] \left[ \begin{array}{cc}
0 & -1\\
1 & 0
\end{array}
\right]
[/tex]

Is the matrix finished there? And could i just put in the points (x,y) into the matrix?

Or could i write?:


[tex]T= \left[ \begin{array}{c}
-x \\
y
\end{array}
\right]
[/tex] [tex] \left[ \begin{array}{cc}
0 & -1\\
1 & 0
\end{array}
\right]
[/tex]

And then put in the x,y if i had the values. Have patience guys I´m a newbie at this...

//Perrry
 
Last edited by a moderator:

Related Threads on Linear Algebra reflection question

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
3
Views
1K
Top