Re: AW: Get theoretical answer on linear equations
- To: mathgroup at smc.vnet.net
- Subject: [mg45147] Re: AW: [mg45122] Get theoretical answer on linear equations
- From: Stefan Fredriksson <stefan at fredriksson.nu>
- Date: Thu, 18 Dec 2003 06:55:22 -0500 (EST)
- References: <3B1F009121A0D411AD7B0010E37C5BEC05A8C777@of-mxs02.oppenheim.de>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Matthias,
Thanks alot for your answer. I have one follow-op question though.
How did you the anser "{{x ->..." formated in such nice way.
I dont get the *'s or a normal / but some strange formatting when I try
to copy or save the answer.
I have Mathematica 4 if it matters.
Regards
Stefan
Matthias.Bode at oppenheim.de wrote:
>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
>
>
>