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Matrix geometric representation

  1. Oct 18, 2006 #1
    Hello all, I have attached a matrix. I am trying to work out this matrix will transform a set of co-ordinates (x_1, y_1, z_1) to a new set of co-ordinates (x_2, y_2, z_2)

    Can anyone give me any hints on how to tackle this problem?
     

    Attached Files:

  2. jcsd
  3. Oct 19, 2006 #2

    HallsofIvy

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    Do you mean that you want to show that this matrix will transform a given set of co-ordinates (x_1, y_1, z_1) to a given set of coordinates (x_2, y_2, z_2)?
    If so, then the obvious: multiply the given matrix by the given (x_1, y_1, z_1) and see that they give (x_2, y_2, z_2). If either set of coordinates is not given then I don't understand what you want to do. Obviously multiplying a matrix by a point (represented as a column matrix) will give another point.
     
  4. Oct 19, 2006 #3
    Sorry, it will be easier if I just post the question.

    What I've done is written two equations

    r2 = r1.A
    r3 = r2.B

    Where A and B are the matrices representing the two transformations.

    Then I have written r3 = r1.A.B
    which expresses the components of r3 in terms of r1.

    After multiplying the two matrices I got the matrix I attached to my first post. However this new matrix looks a little too advanced for what we've been doing in the course. So maybe I've made a mistake?
     

    Attached Files:

  5. Oct 19, 2006 #4
    Nevermind now I have managed to do it.

    r2 = A.r1
    r3 = B.r2

    r3 = B.A.r1

    And I get B.A = (0,1,0), (-1,0,0), (0,0,1)

    Hopefully my notation is okay here, it's meant to read like: (a_11, a_12, a_13), (a_21, a_22, a_23), (a_31, a_32, a_33)

    Which indicates a rotation of 90 degrees clockwise about the z-axis (going from r1 to r3), right?
     
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