  We investigate further the recent proposal for the form of the Matrix theory
action in weak background fields. We perform DVV reduction to the multiple
D0-brane action in order to find the Matrix string theory action for multiple
fundamental strings in curved but weak NS-NS and R-R backgrounds. This matrix
sigma model gives a definite prescription on how to deal with R-R fields with
an explicit spacetime dependence in Type II string theory. We do this both via
the 9-11 flip and the chain of T and S dualities, and further check on their
equivalence explicitly. In order to do so, we also discuss the implementation
of S-duality in the operators of the 2-dimensional world-volume supersymmetric
gauge theory describing the Type IIB D-string. We compare the result to the
known Green-Schwarz sigma model action (for one string), and use this
comparison in order to discuss about possible, non-linear background curvature
corrections to the Matrix string action (involving many strings), and therefore
to the Matrix theory action. We illustrate the nonabelian character of our
action with an example involving multiple fundamental strings in a non-trivial
R-R flux, where the strings are polarized into a noncommutative configuration.
This corresponds to a dielectric type of effect on fundamental strings.
