1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Qucik help with transformation matrices

  1. Sep 19, 2007 #1

    rock.freak667

    User Avatar
    Homework Helper

    1. The problem statement, all variables and given/known data
    Three transformations of the x-y plane are defined as follows.
    [tex]T_1[/tex]: enlargement with centre O(the origin) and scale factor 5
    [tex]T_2[/tex]: Anti-clockwise rotation about the origin O through an angle [tex]tan^{-1}(\frac{4}{3})[/tex]
    [tex]T_3[/tex]: A stretch parallel to the x-axis(with the y-axis invariant) with scale factor 2.

    The transformation [tex]T_4[/tex] is the result of applying [tex]T_1,T_2,T_3[/tex] in that order. Find the matrix which represents [tex]T_4[/tex]


    2. Relevant equations



    3. The attempt at a solution

    [itex] T_1 =\left(
    \begin{array}{cc}
    5 & 0\\
    0 & 5
    \end{array}
    \right)
    [/itex]


    [itex]T_2 =\left(
    \begin{array}{cc}
    cos(tan^{-1}(\frac{4}{3})) & -sin(tan^{-1}(\frac{4}{3}))\\
    sin(tan^{-1}(\frac{4}{3})) & cos(tan^{-1}(\frac{4}{3}))
    \end{array}
    \right)
    [/itex]


    [tex]T_3 =\left(
    \begin{array}{cc}
    2 & 0\\
    0 & 1
    \end{array}
    \right)
    [/tex]

    and [tex]T_4 = T_3*T_2*T_1[/tex]
    Is the matrices I put correct and is [tex]T_4[/tex] correct?
     
    Last edited: Sep 19, 2007
  2. jcsd
  3. Sep 19, 2007 #2

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Other than T2 (which is correct, but should be simplified), you are fine. Transformation matrices chain right-to-left.
     
  4. Sep 19, 2007 #3

    rock.freak667

    User Avatar
    Homework Helper

    so then [tex]T_4[/tex] is just to multiply the transformations in the order given ?
     
  5. Sep 19, 2007 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, that's the whole point- applying the transformation corresponds to multiplying by the matrix.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Qucik help with transformation matrices
Loading...