CHAPTER 5Discrete systems of equations5.1IntroductionIn chapter 3 we considered linear difference equations for a single variable, suchasxt=2xt−1,xt=4xt−1+4xt−2,xt=axt−1+bEach of these equations is linear and autonomous. But suppose we are interestedin such systems as the following:(i)xt=axt−1+byt−1yt=cxt−1+dyt−1(ii)xt=4xt−1+2yt= −2yt−1−3xt−1+3(iii)xt=2xt−1+3yt−1+4zt−1yt=0.5xt−1zt=0.7yt−1All these are examples ofsystemsof linear autonomous equations of the first order.As in previous chapters, we shall here consider only autonomous equations (i.e.independent of the variablet), but we shall also largely restrict ourselves to linearsystems. If all the equations in the system are linear and homogeneous, then wehave a linear homogeneous system. If the system is a set of linear equations andat least one equation is nonhomogeneous, then we have a linear nonhomogeneous
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