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Re: Solving an equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34577] Re: Solving an equation
  • From: N D Evans <nde at eng.warwick.ac.uk>
  • Date: Wed, 29 May 2002 02:44:20 -0400 (EDT)
  • Organization: University of Warwick, UK
  • References: <aci5vg$3c7$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On Thu, 23 May 2002, 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.

I'd be tempted to split this up and use the fact that b and c commute
first:

s1 = Solve[b.c==c.b,Flatten[c]]

and then modify c

c = c /. s1[[1]]

Finally solve your equations

Solve[Flatten[x*a + y*b - c]==0,{x,y}]

to give solution as  {x -> -(b4*c3 - b3*c4)/b3, y -> c3/b3}.  Since b1,
..., b4 and c1, ..., c4 are being treated as parameters the
(degenerate) case b3 = 0 is not treated.  You can then treat the
special cases (b3 = 0, b2 = b3 = 0) separately.  The final
condition that b is not a scalar multiple of the 2x2 identity matrix
should mean that one of these cases holds.

Best wishes,

	Neil.



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