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finding eigenvectors

  • 06-05-2006 3:26pm
    #1
    zap
    Closed Accounts Posts: 839 ✭✭✭


    OK i have an eigenvalue of 1 and i know that i get the original matrix and take it away from the identity matrix so when i do that i get 3 equations


    4x + 4y + 4z = 0
    - 4y = 0
    -8x - 4y - 8z = 0

    now i know that im supposed to perform the elementry row operations on these but what am i working towards 1 letter on each line or whats the story?


Comments

  • #2
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,851 Mod ✭✭✭✭Michael Collins


    You've done most of the work, now you're basically trying to solve three simulations equations. If you did honors leaving cert maths you would have done the same thing.

    Just keep doing your elementary row operations. You'll find that two of the equations actually say the same thing...i.e. one equation adds no new information and reduces to a row of zeros. This is always true when getting eignenvectors (well, it could be more than one). You should find one of the variables is zero (hint: it might be y!!!) and then you should be able to relate x and z in some (pretty simple) way. Then pick a value for one of them (x or z) and the value for the other follows from your simple expression. At first this seems very weird...people usually say "how can I just pick any random value and it'll be right?". The answer is to remember that multiplying an eigenvector by a scalar leaves you with the same eigenvector.

    Good Luck!


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