Re: Solving an equation
- To: mathgroup at smc.vnet.net
- Subject: [mg34495] Re: Solving an equation
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 24 May 2002 02:41:55 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <aci5vg$3c7$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
four equations and two unknows ?
It can't have a general solution
a = {{1, 0}, {0, 1}};
b = {{b1, b2}, {b3, b4}};
c = {{c1, c2}, {c3, c4}};
eqn = Flatten[Thread /@ Thread[ a*x + b*y == c]]
s1 = Solve[Take[eqn, 2], {x, y}]
s2 = Solve[Take[eqn, -2], {x, y}]
s3 = Solve[Take[RotateRight[eqn], 2], {x, y}]
for every solution the remaining two equations are
conditions
(eqn /. Join[s1, s2, s3] // Simplify ) /. True -> Sequence[]
{(b3*c2)/b2 == c3, (b2*c1 - b1*c2 + b4*c2)/b2 == c4},
{(b1*c3 - b4*c3 + b3*c4)/b3 == c1, (b2*c3)/b3 == c2},
{(b2*(c1 - c4))/(b1 - b4) == c2,
(b3*(c1 - c4))/(b1 - b4) == c3}}
Regards
Jens
PSi wrote:
>
> I want to solve the following equation with Mathematica 4.1:
> a*x+b*y=c
> where x, y are the unknown scalars,
> a={{1,0},{0,1}},
> b={{b1,b2},{b3,b4}},
> c={{c1,c2},{c3,c4}},
> the matrices b, c commute, and the matrix b is not a scalar multiple of the unit
> matrix a.
> Could anybody help?