UNIVERSITY OF MANCHESTER
APPLIED NUMERICAL LINEAR ALGEBRA
22 January 2007
Answer ALL five questions in Section A (35 marks in all) and TWO questions in Section B (20
marks each). The total number of marks on the paper is 75. A further 25 marks are available from
work during the semester, making a total of 100.
Electronic calculators may be used, provided that they cannot store text.
1 of 4 P.T.O.
Answer ALL five questions
A1. For a nonsingular matrix A Rn×n
, let Ax = b and (A + A)(x + x) = b + b and suppose
that A A , b b and (A) < 1, where (A) = A A-1
and · denotes any
matrix norm subordinate to a vector norm. Show that