Sparse Linear Equation Solver

I'm trying to solve the set of equations [A][x] = [b], where [A] is known, and some elements of [x] and [b] are known, with the knowns/unknowns corresponding in the following way: (A is a 4x4 matrix in this example)

[A][a1; 1; a3; a4] = [3; b2; 2, 5]

i.e. if the element of a is known, the corresponding element in b is not known, and vice versa. The system I'm trying to solve is very large (1000s by 1000s matrices) and I was wondering what the easiest way to solve this in Matlab would be?

Thanks