3 marks 1. (i) Let A = and x = CO N -2 N Is & in Null(A)? Justify your answer. 2 marks (ii) Consider the transformation T : R2 - R2 defined by r () = [:] Show that T is not a linear transformation.3 marks 2. (i) Suppose that T is a linear transformation with matrix 1 1 A = 2 1 1 2 1 Find a vector 53' for which T(:') = 1 , or show that no such :3 exists. 1 2 1 3 marks (ii) Suppose :31 = 2 and :32 = 1 are eigenvectors of B corresponding to the 1 3 eigenvalues A1 = 1 and A2 = 2 (respectively). Calculate B (:31 + 552). 7 marks 3. Consider the collection of vectors Is B a basis for R4? If not, find a basis for B and determine dim(B). Justify your