There are many libraries you can use. A de facto standard is the LAPACK package with more algorithms you can choose. There are many free and commercial implementations of the same subroutines, for example, OpenBLAS, Intel MKL or Sun Performance Library.
If your system is very large, you would look for some iterative solver. There are many of them, just search for GMRES, BiCGSTAB or similar methods and their implementations (for example, http://people.sc.fsu.edu/~%20jburkardt/f_src/templates/templates.html).