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Solving nonlinear equations using matrix

  1. Feb 2, 2009 #1
    1. To solve for six unknown variables using six nonlinear equations using matrix form and to prooce it as singular.
    Tp1a_d,Tp2a_d,Tp1b_d,Tp2c_d, Tp3b_d,Tp3c_d are known variables
    Tp1,Tp2,Tp3, a,b,c are unknown variables.


    2. Tp1a_d =Tp1+a*Tp1
    Tp1b_d=Tp1+b*Tp1
    Tp2a_d=Tp2+a*Tp2
    Tp2c_d=Tp2+c*Tp2
    Tp3b_d=Tp3+b*Tp3
    Tp3c_d=Tp3+c*Tp3


    3. can I use differential equations to solve these equations?
    But I need to prove that the known variables are dependent on each other by using matrx method.
     
  2. jcsd
  3. Feb 6, 2009 #2

    Tom Mattson

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    Staff Emeritus
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    Gold Member

    That notation is just hideous. Instead I am going to use letters from the beginning of the alphabet (a,b,c,d,e,f) as the known quantities and letters from the end of the alphabet (u,v,w,x,y,z) as the unknowns. Then your system of equations becomes:

    a=u+ux
    c=u+uy
    b=v+vx
    d=v+vz
    e=w+wy
    f=w+wz

    I don't see why you would need to use differential equations or matrix methods. You can eliminate u among the first pair of equations, eliminate v among the second pair, and eliminate w among the third. That will give you 3 equations relating x, y, and z. Use those equations to eliminate 2 variables and solve for the third, and you should be home free.
     
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