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Re: Simultaneous -> Matrix

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  • Subject: [mg113190] Re: Simultaneous -> Matrix
  • From: Peter Breitfeld <phbrf at>
  • Date: Sun, 17 Oct 2010 06:10:16 -0400 (EDT)
  • References: <i9cn12$k6n$>

Brussels Sprout wrote:

> Is there a function for converting a set of simultaneous equations to a matrix equation?

If you want to convert a system of linear equations, you may use
CoefficientArrays as in this little example:

eqs = {a x + b y + c z == u,
  	d x + e y + f z == v,
  	g x + h y + k z == w }


In:= cA=CoefficientArrays[eqs,X]
Out= {SparseArray ....}

Normal makes a Matrix out of the sparse Array and the following will
produce the vector r and the matrix A such that A.X+r==0

In:= {r,A}=Normal[cA]

Out={{-u, -v, -w}, {{a, b, c}, {d, e, f}, {g, h, k}}}

You get the old system of equations back like this:

In:= A.x == -r //Thread

Out= {a x + b y + c z == u,
      d x + e y + f z == v,
      g x + h y + k z == w}

This is the given system eqs.      
Peter Breitfeld, Bad Saulgau, Germany --

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