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!

Find a 2 by 2 matrix such that when cubed, is equal to the identity matrix

  1. Feb 22, 2012 #1
    1. The problem statement, all variables and given/known data
    Find a 2 by 2 matrix such that when cubed, is equal to the identity matrix. This matrix cannot be equal to the identity matrix unless it is cubed.

    So for example:
    B3 = [1 0;0 1]
    but
    B≠[1 0;0 1]

    3. The attempt at a solution
    The professor told us that we have to use a linear transformation where you rotate it three times by 120o. The problem I have is that I cannot visualize how such rotations can solve the problem. Also I don't even know what to rotate. If anyone knows what to do it would be greatly appreciated, thanks!
     
  2. jcsd
  3. Feb 22, 2012 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    What happens when you rotate a vector x by 120 degrees about the origin three times?
     
  4. Feb 22, 2012 #3
    You get back to the original vector. But i still can't relate this to cubing a matrix.
     
  5. Feb 22, 2012 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Think "rotation matrix."
     
  6. Feb 22, 2012 #5

    Deveno

    User Avatar
    Science Advisor

    what you would be rotating is the entire plane, or R2. such a rotation would take the point (x,y) = (1,0) to the point (x',y') = (cosθ,sinθ). that "almost" gives you the matrix right there. use geometry to see if you can figure out where (0,1) might rotate to.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Find a 2 by 2 matrix such that when cubed, is equal to the identity matrix
Loading...