Re: Strange empty set of solutions

• To: mathgroup at smc.vnet.net
• Subject: [mg71805] Re: Strange empty set of solutions
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Wed, 29 Nov 2006 02:56:58 -0500 (EST)
• References: <ekh7pg\$sgs\$1@smc.vnet.net>

M = Table[Random[], {3}, {3}]
{{0.5753783293057292, 0.5655684467176616,
0.6548183854455141}, {0.14136821928006255,
0.6417204506767508, 0.5415326068433255},
{0.8527562576120596, 0.13624503868232524,
0.6691708536378683}}

Solve[M . {a, b, c} == {0, 0, 0}, {a, b, c}]
{{a -> 0., b -> 0., c -> 0.}}

Chop[Solve[M . {a, b, c} == {0, 0, d}, {a, b, c}]]
{{a -> -1.7113533181498632*d, b -> -3.2896639276322523*d, c ->
4.345030307735185*d}}

Chop[Reduce[Reduce[M . {a, b, c} == {0, 0, d} && a^2 + b^2 + c^2 == 1,
{a, b, c}]]]
(d == -0.17506207826755774 && c == -0.7606500358076477 && b ==
0.5758954039731189 && a == 0.299593068525396) ||
(d == 0.17506207826755774 && c == 0.7606500358076477 && b ==
-0.5758954039731189 && a == -0.299593068525396)

Dimitris
> Hi all,
>
> I have a certain 3 x 3 numerical matrix M. If I type
>
> Solve[M.{a,b,c}=={0,0,0},{a,b,c}]
>
> I get
>
> {{a -> 0. + 0.0410026 c, b -> 0. + 1.35294 c}}
>
> However, if I type
>
> Solve[{M.{a,b,c}=={0,0,0},a^2+b^2+c^2==1},{a,b,c}]
>
> I get the empty set. Why is that? I should get two solutions!
>
> Best regards,
>
> Jose Carlos Santos

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