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MathGroup Archive 2006

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Re: Help: How to deal with this problem!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69860] Re: Help: How to deal with this problem!
  • From: dimmechan at yahoo.com
  • Date: Tue, 26 Sep 2006 00:59:16 -0400 (EDT)
  • References: <ef836q$gh8$1@smc.vnet.net>

Supose that you have to solve a 3X3 system e.g.

A = Array[a, {3, 3}]
{{a[1, 1], a[1, 2], a[1, 3]}, {a[2, 1], a[2, 2], a[2, 3]}, {a[3, 1],
a[3, 2], a[3, 3]}}

X = Array[x, {3}]
{x[1], x[2], x[3]}

A . X
{a[1, 1]*x[1] + a[1, 2]*x[2] + a[1, 3]*x[3], a[2, 1]*x[1] + a[2,
2]*x[2] + a[2, 3]*x[3],
  a[3, 1]*x[1] + a[3, 2]*x[2] + a[3, 3]*x[3]}

Solve[A . X == 0, X]
{{x[1] -> 0, x[2] -> 0, x[3] -> 0}}

Solve gives only "generic" solutions. Above trivial solution is valid
when the
determinant of the coefficients matrix A is different than zero.

Use Reduce for complete exploration.

Reduce[A . X == 0, X]


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