OIWQJFEOIWJQEF just figured it out.
for example, in order to find (0,1,0,0), we can say that's
(0,1,0,0) = a(1,1,0,0)-b(1,0,0,0) if we set a=b=1
T(0,1,0,0)=T(1,1,0,0)-T(1,0,0,0)
T(0,1,0,0)=(5,1)-(3,-2)
T(0,1,0,0)=(2,3) which is indeed the answer provided. I just have to do...