6] Form b Q1) If A, B, I are square matrices of size 5x5 with tr(AB) = 4, find tr(2AB + BA + 41).(7 MARKS) Q2) Is the matrix 6B A+ 6AB' hermitian?(show your work).(7 MARKS) 0 1 Q3) Is A = unitary? nilpotent? idempotent? positive semidefi- 10 nite? (show all of your work)(8 MARKS) Q4) If A is positive semidefinite, and so A is unitarily diagonalizable, that is 0 1 250 A = U DU", where U = Find A/2(7 MARKS) 1 0 0 36 3 3 Q5) Let A = Find the singular values of A.(7 MARKS) 3 3 4 0 Q6) Let A= Find || A||2 (7 MARKS) 5 2 (Choose one of the following two questions) Q7) If the eigenvalues of the square matrix A of size 2x2 are 2, 4. Answer the following (7 MARKS) a) Find the eigenvalues of A+ 3 b) Find the determinant of A. 4а аа Q8) Let A = 8 4 1 a, k are real numbers. Is A invertible?(7 MARKS) 5kk 2