problem statement says,

Let

fn = a1 * fn-1 + b1 * fn-2 + c1 * gn-3

gn = a2 * gn-1 + b2 * gn-2 + c2 * fn-3

Find fn % M and gn % M. (% stands for the modulo operation.)

i tried, but can not derive the base matrix.actually i find it difficult when recurrent relation depends on more than one relation.how to derive the base matrix M for this kind of problem where one recurrent relation depends on one or more other recurrent relations?

please help :) :)