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Linear Algebra question

  1. Sep 30, 2006 #1
    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
     
  2. jcsd
  3. Sep 30, 2006 #2
    What's the question?
     
  4. Sep 30, 2006 #3

    radou

    User Avatar
    Homework Helper

    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.
     
  5. Sep 30, 2006 #4
    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
     
  6. Sep 30, 2006 #5

    radou

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    Homework Helper

    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.
     
  7. Oct 1, 2006 #6
    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: Oct 1, 2006
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