1. The problem statement, all variables and given/known data Suppose A is an mxn matrix and b is a vector in R^m. Define a function T:R^n --> R^m by T(x) = Ax + b. Prove that if T is a linear transformation then b=0. 2. Relevant equations For the second part of the question, a transformation is linear if: 1) T(u+v) = T(u) + T(v) for all u,v in domain of T 2) T(cu) = cT(u) for all u & c (scalars) 3. The attempt at a solution For the first part of the question, I am thrown off by the "+b" as I never saw anything other than T(x) = Ax. However, I am leaning towards using the identity matrix I to prove T(x) = Ax, but I don't feel this will be complete... I really need a hand getting started and I think I'll be able to pick it up from there. Thank you!