CS 417/517 Computational Methods and Software
Spring 2004
Solutions to HW 4
Assigned: Thurs Feb 12, 2003; Due: Thurs Feb 19, 2003
1. (a) True, A system of linear equations Ax =bcan have 0,1,∞number of solutions,
depending on whether the matrix Ais singular or nonsingular.
(b) True, The number of solutions to Ax =bcan be determined in some cases ( if Ais non
singular) without knowing the right-hand-side vector b.
(c) True, The 1-norm sums the column, while the inf-norm chooses the maximum absolute
value.
(d) False, If no pivoting, multipliers can be greater than one.
(e) True, Any orthogonal matrix has cond(A) = cond(A−1).
2. kAk1=kAk∞= 23
3. x=[2;2;0] , y=[0;3;0]
4. These matrices are ill-conditioned, any matrix (in the Matlab environment) with condition
number greater than 1012 will be considered to be ill-conditioned.