8 marks 4. Consider the linear transformation T1 from R2 to R2 that corresponds to a reflection across the line 3; = 9:, and the linear transformation T2 from R2 to R2 that corresponds to a reection across the line y = 73:. Let T = T2 0 T1. (a) Find the matrix for T. (b) Calculate T('1) and T('2), where 61 = [a] and E2 = [(1)] What can you say about 51 and EQ in this case? 9 marks 5. Let 1 2 t A: 0 1 3 0 t 1 (a) Are there any value(s) of t which will result in A having a fewer than three distinct eigenvalues (ale. A will have at least one repeated eigenvalue)? If so, nd all such t. Otherwise, show that no such if exists. (b) Find an eigenvector of A corresponding to the largest eigenvalue when t = 1. 9 marks 6. Let z1 = 3 - 3i and z2 = 2 + 2i. (a) Calculate z1 and z2 in polar form. (b) Calculate z122 and express the result in the form a + bi. (c) Calculate ~ and express the result in the form a + bi