1. The problem statement, all variables and given/known data I've posted a few of these recently. I have one question about this problem -- hopefully my calculations are correct. f: R2 to P1, f(a,b)=b+a2x Is this a linear transformation? 2. Relevant equations f(u+v) = f(u) + f(v) f(cu) = cf(u) where u and v are vectors in R2 and c is a scalar. 3. The attempt at a solution let u=(u1,u2) let v=(v1,v2) f(u+v) = ((u2+v2) + (u12x+v12x)) f(u) + f(v) = (u2 + u12x) + (v2 + v12x) So f(u+v) = f(u) + f(v) (First condition met) c(u1,u2) = (cu1,cu2) f(cu) = cu2 + cu12x cf(u) = c(u2 + u12x) = cu2 + cu12x Second condition met. However, my question is -- The question asks is this a linear transformation from R2 to p1. If my calculations are correct, both conditions are met, but the polynomial has a degree of 2, not 1, so it's not a linear transformation from R2 to p1.