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AW: Get theoretical answer on linear equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45145] AW: [mg45122] Get theoretical answer on linear equations
  • From: Matthias.Bode at oppenheim.de
  • Date: Thu, 18 Dec 2003 06:55:19 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello Stefan,

Mathematicas does indeed produce the solution you desire:

Solve[{A1*x + B1*y + C1*z == D1,
A2*x + B2*y + C2*z == D2,
A3*x + B3*y + C3*z == D3}, {x, y, z}]

{{x -> (B3*C2*D1 - B2*C3*D1 - B3*C1*D2 + 
      B1*C3*D2 + B2*C1*D3 - B1*C2*D3)/
     (A3*B2*C1 - A2*B3*C1 - A3*B1*C2 + 
      A1*B3*C2 + A2*B1*C3 - A1*B2*C3), 

   y -> (A3*C2*D1 - A2*C3*D1 - 
      A3*C1*D2 + A1*C3*D2 + A2*C1*D3 - 
      A1*C2*D3)/((-A3)*B2*C1 + 
      A2*B3*C1 + A3*B1*C2 - A1*B3*C2 - 
      A2*B1*C3 + A1*B2*C3), 

   z -> (A3*B2*D1 - A2*B3*D1 - 
      A3*B1*D2 + A1*B3*D2 + A2*B1*D3 - 
      A1*B2*D3)/(A3*B2*C1 - A2*B3*C1 - 
      A3*B1*C2 + A1*B3*C2 + A2*B1*C3 - 
      A1*B2*C3)}}

And it works for larger systems as well!

Best regards,
Matthias Bode
Sal. Oppenheim jr. & Cie. KGaA
Koenigsberger Strasse 29
D-60487 Frankfurt am Main
GERMANY
Tel.: +49(0)69 71 34 53 80
Mobile: +49(0)172 6 74 95 77
Fax: +49(0)69 71 34 95 380
E-mail: matthias.bode at oppenheim.de
Internet: http://www.oppenheim.de




Von: Stefan Fredriksson [mailto:mcriley at telia.com]
Gesendet: Mittwoch, 17. Dezember 2003 13:55
An: mathgroup at smc.vnet.net
Betreff: [mg45122] Get theoretical answer on linear equations


Hi,

I wonder if Mathematica can give me the theoretical answer on linear 
equations. In other words, can it solve these equations without haveing 
the "numbers".

Example:

  I have three equations, and three unknowns;

  EQ1 = A1x + B1y + C1z = D1
  EQ2 = A2x + B2y + C2z = D2
  EQ3 = A3x + B3y + C3z = D3

......and get the theoretical answer;

         A2*D3 - A3*D2   A1*D2 - A2*D1
         ------------- - -------------
         A2*B3 - A3*B2   A1*B2 - A2*B1
    z = -------------------------------
         A2*C1 - A1*C2   A3*C2 - A2*C3
         ------------- - -------------
         A1*B2 - A2*B2   A2*B3 - A3*B2


        (A1*D2 - A2*D1) + (A2*C1 - A1*C2)*z
    y = -----------------------------------
                  (A1*B2 - A2*B1)

        D1 - B1*y - C1*z
    x = ----------------
               A1

I can do this by hand but I need to implement it in a program I write 
and it is so easy to make errors when you solve it by hand. Especially 
since I need the solution for 4,5,6 and 7 equations/unknonws.

I have no idea how to work with matrixs in my programing language so 
please dont give me that as a hint :)

Regards
Stefan


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