1. The problem statement, all variables and given/known data R2 to R1 f(x,y)=xy Determine if the transformation is linear or not 2. Relevant equations T(V1+V2) = T(V1) + T(V2) T(cV1) = Tc(V1) 3. The attempt at a solution If the function f(x,y) = xy we can define another function f(a,b)=ab Therefore, f(x,y) = f(a,b), so xy=ab, so all variables could = each other... T(x*a + y*b) = T(xy) + T(ab) Txa+Tyb = Txy + Tab I'm not really sure if I'm on the right track here. Can anyone help me? I need to know the process for finding whether a transformation is linear or not. Usually, I write another function with a vector similar to the original one, in this case it's ab, then i prove it's one-to-one, then try and prove the other 2 equations. Linear transformations are so difficult and it's so hard to find a good resource online that teaches it simply!