1. The problem statement, all variables and given/known data Derive a formula for T. T([1 1]^T)=[2 -1]^T and T([1 -1]^T)=[0 3]^T (...^T=transpose and T(...)=Linear Transformation 2. Relevant equations T(c1v1+...+cnvn)=c1T(v1)+...+cnT(vn) 3. The attempt at a solution The solutions manual's method and the method I am supposed to use for these problems. Let u1=[1 1]^T and u2=[0 -1]^T. If x=[x1 x2]^T then x=[(x1+x2)/2]u1+[(x1-x2)/2]u2... this is the full solution but I don't know what they are doing here. My question is where did the 1/2's come from? It says to use the equation that have in the relavant equations part, but I don't see how that would get me where they are. Using that I would get... T(u1+u2)=T(u1)+T(u2)=a1u1+a2u2=a1[2 -1]^T + a2[0 3]^T and I am stuck at this point and don't see a connection between what I have and what they have.