Can someone solve 5abc for me please. Hand written solution only

5. (a) Let u1, u2, ... Un E Rm. Let T : R" -> Rm be the transformation defined as T( I) = T = mul+ ruz+ ...+ Inun. . . . Prove that the transformation T is linear. (b) Let 7 1 - 6 , 72 - 1. and -4 1 Now, consider T : R3 - R3 such that T T2 = lul+ Tzu2 + 13 13. Find Ker(T). (c) For T given in part (b): (i) Is T one-to-one? (ii) Is T onto? Be sure to justify your answers