  Yu. I. Merzljakov developed a method of splittable coordinates which helps to
verify the linearity of some groups, he established some fundamental results
using this method. In this paper we use the method of splittable coordinates
and find some sufficient condition under which the semi--direct product of two
linear groups is linear. As consequence we get linearity of some HNN-extensions
of a free group, linearity of the holomorph of the braid group B_n, n >1, and
linearity of some Artin groups. In all cases we construct faithful linear
representations in the explicit form.
