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System of linear equations with complex coefficients

  1. Jul 29, 2009 #1
    1. You have a system of equations of the following form:
    x + iy = 0
    -ix + z = 0
    y - z = 0

    or

    -2Sqr(5)x - iy = 0
    ix - 2Sqr(5)y + 2iz = 0
    -2iy - 2Sqr(5)z = 0




    2. What is the general way in which I can solve such a system? I've tried Kramer's Rule, but it does not seem to work since Dx, Dy, Dz all give zero.
     
  2. jcsd
  3. Jul 29, 2009 #2

    rock.freak667

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    Homework Helper



    Quite easily it can be seen that (0,0,0) is a solution here

    What you can do is form an augmented matrix and row reduce.

    or take the first equation x+iy=0 and put it such that x= -iy and put that into the other equations that have 'x' in it. You will now have two equations with two unknowns.

    Do the same with the other set of equations.
     
  4. Jul 30, 2009 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    . From -ix+ z= 0, ix= z so x= -iz. We also have x= -iy so -iy= -iz or y= z. The last equation is y- z= 0 which says y= z also. That's why all the determinant are 0: this system has an infinite number of solutions. You can choose z to be anything you want and write x and y in terms of z.
     
  5. Jul 31, 2009 #4
    Thank you very much for your answers :smile:
     
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