State space matrices including dirichlet BC

Hello
I want to compute linearized state space matrices of a non-linear system, like incompressible Navier-Stokes discretized with say Taylor-Hood elements. I know how to generate the matrices to obtain a linearized system like

M*du/dt = A*u + B*p
0 = B^T *u

but I want to completely eliminate the dirichlet degrees of freedom for the velocity. If I write velocity as

u = uf + ud

where

uf = free dofs
ud = dirichlet dofs

then I want a system like this

Mf*d(uf)/dt = Af*uf + Ad*ud + B*p

where I simply neglect the term d(ud)/dt. So here Mf, Af are smaller matrices from which dirichlet dofs have been completely removed.

Is there a simple way to construct these matrices ?

Thanks
praveen