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Linear Transformation about the x-axis

  1. Nov 21, 2007 #1
    1. The problem statement, all variables and given/known data

    Find a linear transformation T from R3 to R3 which has the effect of rotating an object clockwise by angle θ around the x-axis.

    2. Relevant equations


    3. The attempt at a solution

    I know that I should work with matrices to show how I came up to the final matrix, which i think has to be the following:

    |x'| | 1 0 0 |
    |y'| = | 0 cosθ -sinθ|
    |z'| | 0 sinθ cosθ|

    However, I dont know how to proceed to show how I came to the following matrix.

    Any help is appreciated..
  2. jcsd
  3. Nov 21, 2007 #2


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    Well, how did you come up with that? Don't you remember what you did? In any case, the problem doesn't really ask you to show how you arrived at that. What you do need to do is show that the matrix has the required properties.
  4. Nov 21, 2007 #3
    Well that is just the solution I have found.

    What do you mean that the matrix has the required properties?

    Do I need to figure out the homogenous equations first?

    I am a bit confused with all these, I've been reading lecture notes and books for ages but none of them seems to make sense to me.
  5. Nov 21, 2007 #4


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    Figure out how (1,0,0), (0,1,0) and (0,0,1) should transform under your rotation. The resulting vectors are the columns of your matrix. Isn't that what you did? Then you are done.
  6. Nov 21, 2007 #5
    So there are no further steps needed to show?

    That's what I did actually....
  7. Nov 21, 2007 #6


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    Not that I can think of. The three basis vectors transform to the correct place. Everything else will just follow.
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