solution to undetermined linear equation

• To: mathgroup at smc.vnet.net
• Subject: [mg83942] solution to undetermined linear equation
• From: shama shahbaz <shammashahbaz at yahoo.com>
• Date: Wed, 5 Dec 2007 07:09:05 -0500 (EST)

```hi

my basic problem is i have a matrix  13*3  of values

-0.2028            0.12778    -0.09129
0.1278             -0.09129    0.07089
-0.09129           0.07089     -0.05731
0.07089            -0.05731     0.04902
-0.05731             0.04902     -0.04188
0.04902             0.04188        0.03747

.............
............

i want to find wieght factors which when applied to above values would result in a value close to 0

such as

-0.2028  g1 +  0.1278  g2 +   -0.09129 g3 +0.07089 g4+........................g13=min
0.12778 g1+-0.09129g2 + 0.07089 g3  +   -0.05731g4+.........................g13=min
-0.09129g1+0.07089g2+   -0.05731g3  +    0.04902 g4+........................g13=min

howeverthe values of g's should be subjected to the constraint

g1+g2+g3+.........................g13=13 and all the wieghts must be nonzero

Is it possible