  Let F_n denote the free group generated by n letters. The purpose of this
article is to show that Hol(F_2), the holomorph of the free group on two
generators, is linear. Consequently, any split group extension of F_2 by a
linear group H is linear. This result gives a large linear subgroup of
Aut(F_3). A second application is that the mapping class group for genus one
surfaces with two punctures is linear.
