1.1 Consider the 2m x 2m matrix A = alm bIm where a, b, c and d are nonzero scalars. CIm dIm 1.1.1 Give an expression for the determinant of A. (7) 1.1.2 For what values of a, b, c and d will A be nonsingular? (5) 1.1.3 Find an expression for A- 1. (10) All 1.2 Let A be an m x m matrix partitioned as A = A12 - where An is mi x mi and An A22 All is rank (A) = rank (An) = mi- 1.2.1 Show that Azz = A21An A12- (8) (0) 1.2.2 Use the result of part 1.2.1 to show that B = is a generalised inverse of (0) A. (8)