1. The problem statement, all variables and given/known data Is T(X,Y)->(X,Y,1) a linear transformation? where X and Y are defined R2 column vectors. 2. Relevant equations Attempt to prove T(cX+Y)=cT(X)+T(Y) Consider T(cx1+y1,cx2+y2)->(cx1+y1,cx2+y2,1) 3. The attempt at a solution RS=cT(x1,y1)+T(x2,y2)->c(x1,y1,1)+(x2,y2,1) =(cx1+y1,cx2+y2,1)+(0,0,c) =(cx1+y1,cx2+y2,1)+c(0,0,1) The 'zero' vector: T(0,0)->(0,0,1) therefore T(cx1+y1,cx2+y2)->(cx1+y1,cx2+y2,1) and T(X,Y)->(X,Y,1) is a linear transformation.