see attached

2) Let V be a vector space over R where dim(V) = n, and let B = {v1, v2, ..., Un} and C = {w1, W2, ..., Wn} be two distinct bases of V (so B * C). For v E V, define the map L : VRn L(v) = [v]B - [v]c where [v] is the coordinate vector of v with respect to basis B and [v]c is the coordinate vector of v with respect to basis C. (a) Prove that L is a linear mapping. (b) Prove or disprove the following statement: "L is an injective linear mapping for any choices of bases B and C." As a reminder, B and C are distinct bases