1. The problem statement, all variables and given/known data If T : V → W is an injective linear transformation, then T^-1: V →W is a linear transformation. 3. The attempt at a solution Let w1, w2 in W. If w1=T(v1) and w2=T(v2), v1=/=v2 in V. Thus, T^-1: V →W is a function. Then, v1+v2=T^-1(w1) + T^-1(w2) and for a in F, T^-1(w1) = aT^-1(w1) = av1 for w in W.