(3.2) Consider the real vector space (R', +, .) with the usual Euclidean metric dR2 (x, y) = |x - yll and define T : R2 - R2 by T(u) = Au where U1 A = so that for any u = ER, T U1 U.2 U2 to (3.2.1) Show that T is a linear operator on R2. (5] (3.2.2) Prove that 72 is a contraction. [7] (3.2.3) Show, by means of an example of vectors u, v E R , why T is not a contraction. (5] (3.2.4) Give a reason why 72 has a unique fixed point and then find this unique fixed point