MATRIX METHODS IN STATISTICS

QUESTION 8 (8.1) For the matrices defined below demonstrate that (A () B) (F ( G) = (AF) ( (BG). (8.2) For the matrices defined below demonstrate that (A () B)-1 = A-1 8) B-1 A = (8.3) Find the characteristic roots of the matrix C defined by 3-B -B C = -B 2B -B -B -B 2B where B= [1 1] (8.4) Find the characteristic roots and associated characteristic vectors of the matrix A given below A = Hint: First find the pattern of matrix A