Let T:R^3 -> R be linear. Show that there exist scalars a, b, and c such that T(x, y , z) = ax + by + cz for all (x, y, z) in R^3. State and prove an analogous result for T: F^n -> F^m. I know that we just have to multiply by a matrix then we can get the desired transformation. But how would I go around to show that such scalars a, b and c exists?