Please clarify the steps

6) For each linea- operato- T on the veater 26 space V, find on ordered bais for the T-cyclie subspace generated by the vector z. a) V=R4,T(a,b,c,d)=(a+b,bc,a+c,a+d), and z=e1. Follow the prove of Theren 5:22. And we know that the dimersion is the maximun number [2,T(z),T2(z),Tt1(z)} is independet and the set is a bais If the subspo Ans Calulate that z=(1,0,0,0),T(z)=(1,0,1,1),T2(z)=(1,1,2,2),T3(z)=(0,3,3,3) So we know the diverion is 3 and the set {2,T(z),T2(z)} b) V=P3(R)T(f(x))=f(x), and z=x3. Ans Calenbete that z=x3,T(z)=6x,T2(z)=0 So we kow that the dimesion is 2 and the set {z,T(2)}isabois. c) V=M22(R),T(A)=At, and z=(0110) Ans that the dimerion is 1 and {z} is a bais. d) V=M22(R)M(A)=(1122)A, and 2=(0110) Coleulate that 2=(0101),T(2)=(1212)T2(2)=(3636) {2,(2)} the dimension is 2 and the set is a basis