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Get theoretical answer on linear equations

• To: mathgroup at smc.vnet.net
• Subject: [mg45122] Get theoretical answer on linear equations
• From: Stefan Fredriksson <mcriley at telia.com>
• Date: Wed, 17 Dec 2003 07:54:37 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: Get theoretical answer on linear equations
    • From: Tomas Garza <tgarza01@prodigy.net.mx>