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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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