Read section 3.e and 3.f v) 1. let v be a vector space and t an operator on v (i. e., a linear map t: v -» suppose that t2 - 5t + 61 = 0, where i is the identity operator and 0 stands for the zero operator. let w3 ve v | tv =3v w2 {ve v | tu = 2v} (a) show that w3 is a subspace of v. (b) show that w3n w2 {0}. (c) for any vector v e v, let v3 = (tv - 2v) and v2 = (3v - tv). show that v3 e w3 and v2 e w2 (d) show that w3 w2 v. (hint: using the notation from the previous part, start by showing that v v32.) w3 w2 (e) use the results of the previous parts to prove that v =