Preparation for Gao's Lemma. Let F be a field and recall the matrices R0=[s0s1t0t1]=[1001],Qi=[011qi]fori=1,2,, and Ri=QiQi1Q1R0F[x]22 for i=0,1,, from the analysis of the traditional extended Euclidean algorithm in Problem Set 1. We also recall that we have the invariants Ri=[sisi+1titi+1]andRi[r0r1]=[riri+1]fori=1,2,,. Show that (a) for all i=0,1,,, we have Ri1=(1)i[ti+1si+1tisi]; and (b) s+1=(1)+1r1/r and t+1=(1)r0/r. Hints: For part (a), observe that detQi=1 and thus det Ri=(1)i. For part (b), apply part (a) to Ri[r0r1]=[riri+1] with i=, recalling that r+1=0