how to improve the condition of matrix

K =

1.0e+007 *

    1.3131   -0.5000   -0.0909    0.3333   -1.2222    0.1667         0         0         0         0         0         0;
   -0.5000    0.6692    0.1667   -0.3636    0.3333   -0.3056         0         0         0         0         0         0;
   -0.0909    0.1667    5.9831   -1.7647   -0.4216   -0.3529   -5.4706    1.9510         0         0         0         0;
    0.3333   -0.3636   -1.7647    2.7558   -0.3529    0.0784    1.7843   -2.4706         0         0         0         0;
   -1.2222    0.3333   -0.4216   -0.3529    2.7574    0.0294    0.2892   -0.1765   -0.0694    0.5000   -1.3333   -0.3333;
    0.1667   -0.3056   -0.3529    0.0784    0.0294    1.2990   -0.1765   -0.4608    0.5000   -0.2778   -0.1667   -0.3333;
         0         0   -5.4706    1.7843    0.2892   -0.1765    5.8708   -1.6684   -0.6894    0.0606         0         0;
         0         0    1.9510   -2.4706   -0.1765   -0.4608   -1.6684    2.9617   -0.1061   -0.0303         0         0;
         0         0         0         0   -0.0694    0.5000   -0.6894   -0.1061    0.8422   -0.2273   -0.0833   -0.1667;
         0         0         0         0    0.5000   -0.2778    0.0606   -0.0303   -0.2273    0.6414   -0.3333   -0.3333;
         0         0         0         0   -1.3333   -0.1667         0         0   -0.0833   -0.3333    1.4167    0.5000;
         0         0         0         0   -0.3333   -0.3333         0         0   -0.1667   -0.3333    0.5000    0.6667;

F =

           0
       37500
           0
           0
           0
       75000
           0
           0
      375000
           0
      375000
       37500
these are my k(12*12) and F(12*1) matrix i  want to find inv(K)*F but it displays bad condition, i have even multiplied by D matrix as stated above,but problem remains there,so pla can u solve this problem

Answer 1

[Sean de Wolski]

Do you have boundary conditions applied to your stiffness matrix? If you don't apply boundary conditions the problem is, by definition, ill-posed and the stiffness matrix will be singular.

Also, use

U = K\F;

instead of inv(K)*F.